First of all, to even be able to find a ghast, you must be able to enter the nether.
See:
If you don't feel like building your own nether portal, you can always join a friend's game or use the tutorial level.
Then, to actually find a ghast, you have to look in specific areas. Ghasts only spawn in at least a 5×4×5 block area and only above ground. So looking over lava pools and in caves is useless.
Once you do find one, killing it with its own fireball can be extremely difficult. You have to hit the fireball while it's in mid-air, and it will fly back in the opposite direction. As long as it hits the ghast, it's an instant kill. To make it easier, you could also use a bow to hit the fireball while it's still near the ghast. Just try to aim it towards the ghast. It may take practice, but once you manage to get the rebounding down, the aiming is easy enough. I recommend trying to get the ghast stuck on something, taking away the need to strafe and jump around to hit the ghast.
Video credit goes to SkilledWhacky