Successfully complete the Madd Dogg's mission "Vertical Bird" to gain access to the Hydra fighter jet located at the abandoned airstrip in the hanger. Alternately, to get the Hydra earlier in the game, when you are able to enter the Las Venturas airport, after you have passed the flying school, just ahead the entrance (inside the airport) to your right is a red circle where you can race with different airships and choppers. In one of this races you can play with the Hydra. Put it inside the hangar at the abandoned airstrip, get out of the plane, and wait until the timer is over. When done, the Hydra will still be inside the hangar. This can be done with any of the vehicles of those races. The Hydra also spawns at the army ship where you have to get it in this mission down at Easter Basin. You can also get it by entering the races in Las Venturas airport, then using the "Keep aircraft from races" trick. Press B while in it to fire the rockets. Check the very bottom/end of the underground police garage in San Fierro to find a Hydra. You will need a police vehicle to get the guard to let you in (and avoid a three star wanted level). After completing the Vertical Bird mission, the Hydra will appear at the abandoned airstrip.

The controls for the Hydra are as follows:

Lift: Hold A.
Flares: Press B.
Forward: Press Left Analog-stick Forward until the nose points down slightly then press A.
Lock And Shoot: Hold R until the reticule turns red, then press L.
Wheels Up: Click Right Analog-stick.
Rotate: Hold White or Black.
Look At Yourself: Press White + Black.