To steal the P-996 LAZER fighter jet first steal any car, preferably fast, and go to Los Santos Customs. Upgrade the car with more power and armor. This way when you enter the military base you can avoid the military more easily.

Shooting Range Guide
Landing a Plane Safely

Military Base Location

Go to the military base at Fort Zancudo which is north of Los Santos:

The location of the military base is at Fort Zancudo north of Los Santos.

Drive as fast as you can through the gates. Drive through the car park and between two concrete blocks that are standing far enough apart for you to get through:

Drive through the gap between the concrete blocks.

Go left past the building and through the fence.

P-996 LAZER Fighter Jet Location

The fighter jet is in the open hangar down the runway ahead:

The P=996 LZAER fighter jet is located in the open hangar ahead.

Once in the plane you can take off within the space between it and the grass. Once you are in the air fly around to lose the cops but be sure to fly high enough so the helicopters don’t spot you.