Years ago, when I lived in California, all you needed was to go to a police establishment and tell the detectives on duty that you possess a gun, how you got it, and that you want it registered in your name.
Nowadays, things might be a little more complicated.
The gun is yours by right of possession. As long as its serial number doesn't come up on a "stolen" list, your ownership and possession are legally assured.
But now California has a lot of laws that restrict things like magazine capacity, and, more recently, even the make and model of the gun.
So if you walk into a police station with it (if that's still required—or allowed) you had better first make sure that the pistol meets all of the new legal criteria.
It doesn't matter that you were given this handgun 20 years ago. The operative issue is that you seek to register it right now. The requirements of 20 years ago are no longer the controlling factors. Only the laws at the time you seek to register it will apply.
I strongly suggest that you consult an attorney on this matter.
Failing that, ask at a local gun shop to find out what the legal restrictions are.
Worst case, you can do your own research by consulting the laws of California, either in your county's law library or on-line.
(How about posting the make and model of the gun, right here in this forum thread?)