When your turn begins, you will be given a certain number of guys, based on what 'hoods you own and how long you have owned them. You will see them appear in the section of the screen directly below the television in the upper right hand corner.
You can place those guys simply by selecting the guys you want, and then once selected, clicking on any hood you own.
Some very useful keyboard shortcuts are:
Hold down the SHIFT key and you will place all of your guys.
Hold down the OPTION key and you will place one of your guys.
Hold down the CONTROL key and you will place half of your guys.
These shortcuts also work when attacking or fortifying.
 
Fighting
After you've placed your guys, you can move and fight. You can attack any hood adjacent to yours. Hoods across the water from each other are adjacent if connected by a bridge or tunnel or line. There are two airports on the map (indicated by the airplane symbol), one in central New Jersey and one in eastern Brooklyn. Your guys can move from one airport to the other as if the two airport hoods were adjacent.
To find out about a hood, command-click on it.
1) Click on the hood you want to attack from.
2) Click on the enemy hood you want to attack.
3) Watch the bullets fly!
 
4) If you win, your troops move into the new hood, leaving one guy in the hood you attacked from.
To move less guys from your hood, hold down the control key to attack with half your guys, and hold down the option key to attack with one guy. To attack with all of your guys (usually the default) hold down the shift key when you attack.
You can also use the mouse to select the guys you'll leave in the hood you're attacking from. When you click on a guy, he is highlighted. You'll leave the highlighted guys behind.
Combat is fought in rounds. The result of each round is somebody getting whacked, one of your guys or, (preferably), one of your rivals'. Combat is pretty evenly matched. In any round, there's a 50.5 percent chance that the attacker will lose a guy, and a 49.5 percent chance that the defender will lose a guy. Don't be fooled by these close numbers though, over the course of a game it can make a real difference. If you made any players lucky, the odds are tilted in their favor.
You must attack an empty hood with at least three guys. One you lose getting rid of the local street gangs. (like the Jets and the Sharks), one stays in the hood you're attacking from and one moves into the empty hood.
Fortifying
After you've finished all fighting, if you want to reposition any of your guys, click "Fortify." If you just want to end your turn, click "End Turn."
 
If you clicked "Fortify", you can now move your guys from any of your hoods to any other contiguous hood. You can move your guys as many times as you like. But remember, for all of yous who don't know what "contiguous" means, if you own hoods that aren't connected either directly or by through other hoods you own -- you can't swap guys between 'em!