One of the biggest ways Civ4 is different from Civ3 is in the way we choose locations for cities.
In Civ3, city placement was a sort of checklist, and the cities with the most checks were usually the best. Fresh water, check. Hills/mountains for production, check. Food tiles for growth, check. Resources, check. On the coast, check. And so on; you wanted the best checklist cities possible because with the exception of cultural victory cities and maybe super science cities (with double sci wonders), all cities really did the same thing. This is not so in Civ4, and when I first made the transition the need to specialize cities was one of the things that was most confusing to me. But I'm getting ahead of myself.
Why Specialize?
There are a number of factors that force us to specialize our cities. They are, in no particular order:
-Great People system. The nature of GP makes it far more beneficial to have one city produce a ton of GPP than have a bunch of cities all make a little bit of GPP.
-Roads no longer produce commerce. In Civ3, we didn't need to make commerce-specific cities because every large, fully roaded (or RRed) city produced a lot of commerce on its own. This is not so in Civ4; you need to build a specific improvement (cottage) in order to increase a tile's commerce.
-National wonder complement each other, but you can only build 2 per city. It is a great idea to have Heroic Epic and West Point in the same city; it will build military units faster and give them bonus experience to boot. Since the national wonders usually give a percent benefit to one aspect of a city's production, it obviously behooves us to ensure that the aspect recieving the bonus is as high as possible.
-# of city upkeep forces us to limit the number of cities we found. This is probably the biggest difference from Civ3. There was a penalty from founding too many cities in Civ3 (corruption), but it was nowhere near as crippling as the penalty is in Civ4. Since we are severely limited in the number of cities we can make, we obviously want to make the most of those cities. (One thing that strikes me as odd about this is the dissolution of colonies in Civ4. If the game is designed to discourage founding a city specifically to get an important resource, shouldn't there be a built in alternative?)
-Culture provides a defensive bonus. This means that in addition to any logistical benefits, a few high culture cities will always be easier to defend than a horde of low culture cities.
-Religion! Simply put it is easier to spread religion to all of your cities if you have less cities.
So now that we have a good idea of why it specializing is good, lets look at the three basic types of cities.
The House of Commerce, aka Moneybag City, Goldsville
Essentially, this is a city that is designed to get as much commerce as possible. You will end up building cottages on almost every tile in the city's fat t, but it is important to have enough food to ensure that the city grows quickly. This city will have lots of gold (and therefore science), so it behooves you to build +% gold/science improvements here (depending on what you are doing at the time)!
When looking for places for commerce cities, remember that while eventual gold production is important, you also need to consider the speed at which the city will reach its optimal size. You could have the highest gold city in the world and it would be useless if it takes all game to get to size 6.
You have to balance this need for food with early cottage placement, however. Cottages take a long time to grow fully, and need to be worked in order to grow. You need to be wary of the opposite of the high-gold-no-people commerce city; the high-people-no-towns commerce city. Balance working food tiles and cottages while your commerce city grows.
Consider rivers carefully. Rivers provide a bonus to both commerce and, through farming, food. You need to decide whether to use a river for your commerce city or for...
The GP Farm aka Specialistville, Wondertown.
This city is built on pure population, converted into specialists to produce GPP. In low levels you can usually count on wonders to produce a good amount of GPP, but specialists are more reliably attainable and above all, convertable.
Look for fertile ground with lots of bonus food. If you also want to get wonders for GPP, you will need a good amount of production as well, so some hills would probably be nice too.
Obviously, it would be a good idea to get +GPP improvements/wonders here. National Epic (I think thats what it's called) should go here for sure.
One more thing - never put super-specialists in your GP Farm. GP Farms usually produce a fair amount of culture/beakers/commerce just by having so many specialists, but never forget that their primary purpose is making GP. Put the super-specialists in a place that could really use the extra production, like...
The Factory, aka Anviltown, Hill-Land, Detroit
What the house of commerce is for money and the GP farm is for food, the factory is for production. This city, when fully developed, should be capable of producing a ton of hammers per turn, and be fully endowed with national wonders that increase either production or the benefits of it. I have already mentioned my personal favorite combination of nat'l wonders for the factory: Heroic Epic and West Point. Other combinations are possible too, most using Iron Works in some way. It is sometimes necessary to distinguish between a military factory and a wonder/SS/other factory.
What I said about the commerce city and growth holds true for the factory as well; you need to emphasis production, yes, but the city also has to grow. Remember, you can put a factory on the coast too, for mass production of ships.
In Civ3, city placement was a sort of checklist, and the cities with the most checks were usually the best. Fresh water, check. Hills/mountains for production, check. Food tiles for growth, check. Resources, check. On the coast, check. And so on; you wanted the best checklist cities possible because with the exception of cultural victory cities and maybe super science cities (with double sci wonders), all cities really did the same thing. This is not so in Civ4, and when I first made the transition the need to specialize cities was one of the things that was most confusing to me. But I'm getting ahead of myself.
Why Specialize?
There are a number of factors that force us to specialize our cities. They are, in no particular order:
-Great People system. The nature of GP makes it far more beneficial to have one city produce a ton of GPP than have a bunch of cities all make a little bit of GPP.
-Roads no longer produce commerce. In Civ3, we didn't need to make commerce-specific cities because every large, fully roaded (or RRed) city produced a lot of commerce on its own. This is not so in Civ4; you need to build a specific improvement (cottage) in order to increase a tile's commerce.
-National wonder complement each other, but you can only build 2 per city. It is a great idea to have Heroic Epic and West Point in the same city; it will build military units faster and give them bonus experience to boot. Since the national wonders usually give a percent benefit to one aspect of a city's production, it obviously behooves us to ensure that the aspect recieving the bonus is as high as possible.
-# of city upkeep forces us to limit the number of cities we found. This is probably the biggest difference from Civ3. There was a penalty from founding too many cities in Civ3 (corruption), but it was nowhere near as crippling as the penalty is in Civ4. Since we are severely limited in the number of cities we can make, we obviously want to make the most of those cities. (One thing that strikes me as odd about this is the dissolution of colonies in Civ4. If the game is designed to discourage founding a city specifically to get an important resource, shouldn't there be a built in alternative?)
-Culture provides a defensive bonus. This means that in addition to any logistical benefits, a few high culture cities will always be easier to defend than a horde of low culture cities.
-Religion! Simply put it is easier to spread religion to all of your cities if you have less cities.
So now that we have a good idea of why it specializing is good, lets look at the three basic types of cities.
The House of Commerce, aka Moneybag City, Goldsville
Essentially, this is a city that is designed to get as much commerce as possible. You will end up building cottages on almost every tile in the city's fat t, but it is important to have enough food to ensure that the city grows quickly. This city will have lots of gold (and therefore science), so it behooves you to build +% gold/science improvements here (depending on what you are doing at the time)!
When looking for places for commerce cities, remember that while eventual gold production is important, you also need to consider the speed at which the city will reach its optimal size. You could have the highest gold city in the world and it would be useless if it takes all game to get to size 6.
You have to balance this need for food with early cottage placement, however. Cottages take a long time to grow fully, and need to be worked in order to grow. You need to be wary of the opposite of the high-gold-no-people commerce city; the high-people-no-towns commerce city. Balance working food tiles and cottages while your commerce city grows.
Consider rivers carefully. Rivers provide a bonus to both commerce and, through farming, food. You need to decide whether to use a river for your commerce city or for...
The GP Farm aka Specialistville, Wondertown.
This city is built on pure population, converted into specialists to produce GPP. In low levels you can usually count on wonders to produce a good amount of GPP, but specialists are more reliably attainable and above all, convertable.
Look for fertile ground with lots of bonus food. If you also want to get wonders for GPP, you will need a good amount of production as well, so some hills would probably be nice too.
Obviously, it would be a good idea to get +GPP improvements/wonders here. National Epic (I think thats what it's called) should go here for sure.
One more thing - never put super-specialists in your GP Farm. GP Farms usually produce a fair amount of culture/beakers/commerce just by having so many specialists, but never forget that their primary purpose is making GP. Put the super-specialists in a place that could really use the extra production, like...
The Factory, aka Anviltown, Hill-Land, Detroit
What the house of commerce is for money and the GP farm is for food, the factory is for production. This city, when fully developed, should be capable of producing a ton of hammers per turn, and be fully endowed with national wonders that increase either production or the benefits of it. I have already mentioned my personal favorite combination of nat'l wonders for the factory: Heroic Epic and West Point. Other combinations are possible too, most using Iron Works in some way. It is sometimes necessary to distinguish between a military factory and a wonder/SS/other factory.
What I said about the commerce city and growth holds true for the factory as well; you need to emphasis production, yes, but the city also has to grow. Remember, you can put a factory on the coast too, for mass production of ships.
).
Also, sometimes after you research a new building becomes available, and sometimes it is more efficient to drop down your science bar for two turns so you can hurry the production of the new building in every city you have, and then return things to what they were doing before. 
