Each area of the game is controlled by a gang run by one of your rivals. In each area there are set places (nests) where gang members meet up and generally hang around hoping that you turn up, presumably. Once you've found one of these gangs, you can either try to intimidate them for extra balls and to decrease gang heat, or kill them, the latter being the preferred method. At the start of the game these gangs are pretty rubbish with just a couple of guys with guns and the rest just trying to punch you so they're not going to cause you a lot of trouble. Later gangs however, are little armies complete with bazookas, machineguns and over 30 members.
Preparation
It's best to come prepared. Call a driver first. This does two things: gives you a second man to help take on the gang and once inside the car gives you some extra armour. Also, make sure you've got some pretty good weapons on you. All this effort does not go unrewarded; gangs will leave money, coke, balls and even give you turf in disputed areas. Note that you can only wipe out gangs in Owned or Disputed areas; if you take out a gang in another area it'll be nothing but a hassle and they will reappear. Also, if you let gang members get away after wiping most of them out they will reappear.
Locked and unlocked turf
You can only wipe out gangs from areas that are marked Contested or Owned. Attempting to take out a gang from a Locked area (including the Industrial Zone, Trailer Park, and the Islands, which are always locked) will simply cause them to respawn later.
Active and inactive gangs
Once you've found a gang area, it'll appear on the map as a Skull, however these gangs won't always be active and then they'll appear as a shaded Skull. It's best to wait a while until the gang turns up.
Gang Heat
As with Cop Heat, gangs have their own heat meter. This increases as you kill more gangs, and generally do any of the missions in the game. For the most part this gang heat is nothing to worry about, but higher Gang heat levels means it'll be harder to perform coke runs, gangs will attack on sight and if the meter rises to full, a gang retaliation is certain, which includes attacking your fronts, car bombs and drive-bys.
Dealing with Gang Heat
The main way to lower Gang Heat is pay off Vice. Press 
, select Empire, then Heat, select Gang Heat and then press 
to pay to have your heat lowered. The higher the heat and your reputation, the more you'll have to pay.
Besides paying Vice, there are other ways to deal with Gang Heat. You can find and intimidate gang members (like supplier bodyguards) using the meter to lower your heat a little. Completely wiping out gangs from Contested or Owned areas will reduce heat as you clear enemies from your turf.
One of the better ways to lower Gang Heat is to hire an Enforcer, who becomes available at Reputation Level 2. Most of his missions will involve attacking gangs; succeeding usually results in reduced heat.