Get to a rail station, elevated rail station, or trolley, then get in and wait until your wanted level goes down.
To avoid the police, make a lot of turns. The most effective turns are in front of or behind another car or the trolley. The police will try making your exact turn, but will run into the car or trolley. You can also make turns between light posts close to the curb if your car is small or short enough. This also works well during the first mission.
If you have a gun and the cops are after you, get rid of them by shooting them. This takes some practice, but it can be done. You have to be on foot. Shoot both cops until their weapons fall. Head shots work best. If you manage to kill both advancing officers, you will no longer be wanted. This works better if there is only one car after you (the offense does not matter). The more the cars, the more difficult it is.
When caught driving fast and a cop is chasing you, get out of the car when the police are far behind. The cop gets confused and the wanted bar will disappear quickly if you hide away from the road. If you are caught on foot, get in a vehicle and quickly get out of the area. Park it in a quiet place and wait in the car until the wanted bar disappears. Note: A cop can determine your speed only when you cross him. You might run at high speed but make sure you slow down before you pass by a cop vehicle or a cop on foot.