Ok, sorry to ask this, but I downloaded the Basic strategy PDF from here and I still can't figure this out.

On tiles around the cities, after I build a farm or a mine, or a cottage with my Worker and I build a road for it, does that mean it starts providing me with production or commerce, etc? I keep having the feeling that I am missing something.

And in the city screen, I can + or - Citizens. What is that for? I know how the scientists and others work, but I'm not sure what citizens do.

Sorry for the dumb questions guys, but please help.

If in doubt, look in the civopedia (F12) which is 99% right about most things.

To answer your questions, firstly, roads are only needed to hook up resources and get their benefits -- i.e. a road from your city to a gold mine would give you the +1:) to that city and any others that are on your network. You do not need roads over regular improvements like farms, cottages, and mines. Once they are built, that's it.

Citizens are basically just generic specialists and really should be avoided. They give +1:hammers: to your city, but no :gp:, so don't ever use them (unless you really know what you're doing, and need that extra +1 :hammers: but that's another story). Any random square in your city radius or empty GP slot will almost certainly be a better option. You'll notice that when your city grows unhappy, you get an angry citizen that you cannot get rid of until the city becomes happy again. Try to avoid this by using slavery or increasing your happy cap by gettin more :) resources (with roads, or via trade deals). But yeah, check F12 for this kind of thing.