There's a couple of different ways of doing this, depending on the type of vehicle and who is driving it.
If it's an "non-hostile" driving, (even cops and gang members, so long as they're not angry with you) and they haven't yet panicked, you can usually pull over in front of them, and they'll stop. Gunfire and damage to cars, or other hostile actions will cause them to panic - speed up and drive faster than the car should be able to drive, with no regard for the safety of themselves or others.
If the car in question is hostile, you've got a few choices.
- If you're behind them and coming up on them, you can slam your front wheel into their rear wheel. This is actually a real police tactic, and it's called the PIT maneuver. It doesn't work as well in this game as it does in real life, but it's often effective when you're trying to stop someone from fleeting.
- Throw an electronic grenade at the car, which will stun it temporarily. I don't believe this will (generally) raise your wanted level, but it is considered hostile, so if you've got no wanted stars, this will likely give you one.
- Get out in front of the car, and hop out of your car (making it into a car torpedo) and then press "Sprint" + "Steal Car" which will cause you to jump through the windshield. If there are multiple people in the car, the others will get out, even if they're manning the gun on an APC, for instance. (For tanks, you have to kill the gunner first)
- The RC Possessor (which you get at the end of Act 1) will allow you to stop cars. Generally when you exit the remote control interface, the driver will just hop out. This works for helicopters and VTOLs as well. I don't think you can do this while driving, but it has a long range so you can get out in front of a car, jump out of whatever you're driving, and take control of it as it's chasing you. If you level it up, you can cause cars to explode when you take control of them, which will insta-kill any brutes or specialists in the vehicle.
- Explosive weapons, especially the Annihilator, will destroy most cars with one hit. Your wanted level will probably go up, however. For dealing with gang cars featuring brutes and/or specialists, this is one of the best solutions.
- Shooting the driver is possible, use something pretty accurate though, like the pistols. This can be tricky while you're driving.
- You can shoot the wheels, the effect of this is that the car is harder to control. You'll want to maintain high speeds and/or turn corners frequently to shake a car that's been damaged in this way.
If you're having trouble doing this while driving, you might want to look into the cruise control feature. It's not perfect, but it can take one button off your list of things to be pressing at the same time. If you can find a co-op partner, most of the time the tasks will be divided between you, so one of you can focus on driving the car and the other on taking out pursuing vehicles.
Remember also that losing your wanted level is really easy in this game - visit any owned shop or crib and you'll magically, instantly, lose your wanted level. Plus, there are "homies" you can unlock that give you this option anywhere.
If the game is feeling "hard" - (ie, gang wanted level is tearing you up, or brutes are really difficult) go progress the plot or play some of the easier activities. In the meantime, invest your money in buildings you can own, damage reduction/health increasing upgrades, and upgrading one or two weapons.
Later in the game you will have many more tools for doing damage and avoiding the law/gangs. if there's something in particular that's got you stuck, put it aside, since by the end of the game you will easily be godlike, and you can use your powers to finish off anything that was tricky before.