Cracker may have covered some of this in his article on workers, but in light of a recent discussion elsewhere I'll post this here.
Once you learn Engineering you can plant forests. Why would you want to do this?
Generally players like to emphasize growth over production immediately, as with "emphasize" production on, you'll get much of this back, and you'll get more commerce by growing faster. But, pre-aqueducts and pre-hospitals growth has its limits. All too often, in my opinion, it seems that players will end up with cities that can't grow and have several extra foods in their box. Here's an example
http://i370.photobucket.com/albums/oo146/Spoonwood792000/1241231958.jpg. Experienced players may correctly guess that I've got a 20k game going here... so at *that* time I couldn't really do much with forests, but the actual game itself is probably unusal in this respect and I only wanted it as an example here.
But, suppose it were the middle ages and I was building Copernicus's Observatory or a University instead of The Great Library (both cost 400 shields), and I had Engineering. Warmongers may want to suppose they're building The Heroic Epic, The Military Academy, the Pentagon, knights, cavalry, or armies. Also suppose that I'm a Republic or Monarchy and use the wheat square instead of a bonus grassland.
In such a case, without any more forests, I would have 7 extra food in the box not doing anything for me. In this game, I can plant a forest on two of the non-bonus grasslands, two of the wheats, and both cows for an extra shield in each square. That's 6 extra shields per turn, which would slice Copernicus's Observatory, an army, the Military Academy, or the Pentagon... each of which cost 400 shields... down from 19 turns to 15 turns. A (non-scientific) university or The Heroic Epic would drop from 10 turns to 8 turns. Knights and Cavalry would drop from 4 to 3 turns. This example implies that it (often) pays off to forest squares once your cities hit size 12 and you have Engeering that it pays off to forest *regular* grassland spots, grassland wheat, and grassland cow squares (as well as grassland wine squares, and other luxuries also).
Similarly, cities without freshwater or an aqueduct that hit size 6 (and don't have too much corruption) might also have plenty of extra food in the box. Similarly, you can forest squares in those cities for a little extra production. Maybe you plant forests and chop towards aqueducts. This leads me to the subject of forest chopping.
As John Sheppard might say "I needed lumber for my army" (this appears in an episode of Stargate: Atlantis which supposedly got inspired by the civilization series). I mean to say that every flatland square potentially provides 10 extra shields for your armies, or for your buildings. The only problem comes as that you can only chop a forest in a flatland square *once*, and you probably don't want to waste worker moves. Maybe you have a really good memory, but I certainly have trouble remembering *every* square as to whether I've chopped it yet or not. Cracker recommends taking screenshots of your games so you know which square you've chopped. Elear recommended to me the following tactic in a succession game which he says has been around a while (perhaps I've expanded on it below)...
Basically, one re-names cities according to which squares you've chopped with numbers. To do this easily, you'll want short city names. I recommend using numbers for your cities, so you know how many cities you have (useful for knowing how many armies you can train, how many more cities you have until the forbidden palace). If you find this too mechanistic, I recommend at least trying to keep your city names as short as possible when using this re-naming tactic. Here's a screenshot, which I'll basically explain my proccess below.
http://i370.photobucket.com/albums/oo146/Spoonwood792000/1241231959.jpg
Now, let's say I have a forest in the spot where if I work a unit in the city, I would hit the '9' button on the keypad. Let's say I want to chop that forest. When I direct my worker to chop that forest, I'll then rename my city from say "003, to 003 9". If I were then to chop a forest in a square which required me to hit 9 two times after that, I would rename the city from "003 9" to "003 9 99". If I had to hit 74 to move a horseman from the city center to the spot I'm chopping, I would rename the city "003 9 74 99" (or 47 instead of 74, it doesn't matter). Later on, I might have "003 3 9 36 74 99" as the city name. You can try this too. The only problem comes as that you can only have so many characters in your city names, so after a while you can't put in any more numbers. At this point, you'll probably have several single numbers and several double numbers. So, eliminate the spaces. This might mean you have "003 123679 33367499" as the city name, meaning you've chopped square 1, 2, 3, 6, 7, 9, 33, 36, 74, and 99. Eventually, this will even run out of space. Hopefully, by this point, either you've chopped all single number *flatland* squares or all double numbered *flatland* squares with only the other ones remaining. At this point (or a little earlier) you can replace whichever set of square full with an "f" for full... such as "003 f 3336749699" meaning I've chopped all one-movement squares and only have 2 movement squares left not indicated. "003 123678 f" would mean I have only one-movement squares 4 and 9 left to chop and have chopped all two-movement squares. If you look carefully at the screenshot above, you can actually see I can replace some of those numbers with "fs" but I didn't do so, since I have mountain squares around.
While writing this I thought of another use of forests, which I haven't really used, but may work well. It's probably more intensive to use than either of the above tactics. Suppose you have no two or three potential production squares you're not using once you have engineering. Plant a forest in the city radius and do NOT use it as your city grows. If you have "emphasize production" on in the city governor screen and everything else off (as seems fairly normal), ignoring corruption, you'll get two extra shields as the city grows. Then reconfigure the city on the next turn.
Once you learn Engineering you can plant forests. Why would you want to do this?
Generally players like to emphasize growth over production immediately, as with "emphasize" production on, you'll get much of this back, and you'll get more commerce by growing faster. But, pre-aqueducts and pre-hospitals growth has its limits. All too often, in my opinion, it seems that players will end up with cities that can't grow and have several extra foods in their box. Here's an example

http://i370.photobucket.com/albums/oo146/Spoonwood792000/1241231958.jpg. Experienced players may correctly guess that I've got a 20k game going here... so at *that* time I couldn't really do much with forests, but the actual game itself is probably unusal in this respect and I only wanted it as an example here.
But, suppose it were the middle ages and I was building Copernicus's Observatory or a University instead of The Great Library (both cost 400 shields), and I had Engineering. Warmongers may want to suppose they're building The Heroic Epic, The Military Academy, the Pentagon, knights, cavalry, or armies. Also suppose that I'm a Republic or Monarchy and use the wheat square instead of a bonus grassland.
In such a case, without any more forests, I would have 7 extra food in the box not doing anything for me. In this game, I can plant a forest on two of the non-bonus grasslands, two of the wheats, and both cows for an extra shield in each square. That's 6 extra shields per turn, which would slice Copernicus's Observatory, an army, the Military Academy, or the Pentagon... each of which cost 400 shields... down from 19 turns to 15 turns. A (non-scientific) university or The Heroic Epic would drop from 10 turns to 8 turns. Knights and Cavalry would drop from 4 to 3 turns. This example implies that it (often) pays off to forest squares once your cities hit size 12 and you have Engeering that it pays off to forest *regular* grassland spots, grassland wheat, and grassland cow squares (as well as grassland wine squares, and other luxuries also).
Similarly, cities without freshwater or an aqueduct that hit size 6 (and don't have too much corruption) might also have plenty of extra food in the box. Similarly, you can forest squares in those cities for a little extra production. Maybe you plant forests and chop towards aqueducts. This leads me to the subject of forest chopping.
As John Sheppard might say "I needed lumber for my army" (this appears in an episode of Stargate: Atlantis which supposedly got inspired by the civilization series). I mean to say that every flatland square potentially provides 10 extra shields for your armies, or for your buildings. The only problem comes as that you can only chop a forest in a flatland square *once*, and you probably don't want to waste worker moves. Maybe you have a really good memory, but I certainly have trouble remembering *every* square as to whether I've chopped it yet or not. Cracker recommends taking screenshots of your games so you know which square you've chopped. Elear recommended to me the following tactic in a succession game which he says has been around a while (perhaps I've expanded on it below)...
Basically, one re-names cities according to which squares you've chopped with numbers. To do this easily, you'll want short city names. I recommend using numbers for your cities, so you know how many cities you have (useful for knowing how many armies you can train, how many more cities you have until the forbidden palace). If you find this too mechanistic, I recommend at least trying to keep your city names as short as possible when using this re-naming tactic. Here's a screenshot, which I'll basically explain my proccess below.

http://i370.photobucket.com/albums/oo146/Spoonwood792000/1241231959.jpg
Now, let's say I have a forest in the spot where if I work a unit in the city, I would hit the '9' button on the keypad. Let's say I want to chop that forest. When I direct my worker to chop that forest, I'll then rename my city from say "003, to 003 9". If I were then to chop a forest in a square which required me to hit 9 two times after that, I would rename the city from "003 9" to "003 9 99". If I had to hit 74 to move a horseman from the city center to the spot I'm chopping, I would rename the city "003 9 74 99" (or 47 instead of 74, it doesn't matter). Later on, I might have "003 3 9 36 74 99" as the city name. You can try this too. The only problem comes as that you can only have so many characters in your city names, so after a while you can't put in any more numbers. At this point, you'll probably have several single numbers and several double numbers. So, eliminate the spaces. This might mean you have "003 123679 33367499" as the city name, meaning you've chopped square 1, 2, 3, 6, 7, 9, 33, 36, 74, and 99. Eventually, this will even run out of space. Hopefully, by this point, either you've chopped all single number *flatland* squares or all double numbered *flatland* squares with only the other ones remaining. At this point (or a little earlier) you can replace whichever set of square full with an "f" for full... such as "003 f 3336749699" meaning I've chopped all one-movement squares and only have 2 movement squares left not indicated. "003 123678 f" would mean I have only one-movement squares 4 and 9 left to chop and have chopped all two-movement squares. If you look carefully at the screenshot above, you can actually see I can replace some of those numbers with "fs" but I didn't do so, since I have mountain squares around.
While writing this I thought of another use of forests, which I haven't really used, but may work well. It's probably more intensive to use than either of the above tactics. Suppose you have no two or three potential production squares you're not using once you have engineering. Plant a forest in the city radius and do NOT use it as your city grows. If you have "emphasize production" on in the city governor screen and everything else off (as seems fairly normal), ignoring corruption, you'll get two extra shields as the city grows. Then reconfigure the city on the next turn.