You didn't specifiy what you wanted to register. Assault Weapons and handguns are different, but you do not need to register non-AW long guns. The posted CA code for importing an AW applies, but it doesn't show you what you're up against.
Getting a CA-DOJ AW permit has the same requirements as a machine gun permit, they are difficult to obtain, expensive to maintain and are only issued to those actually doing business in that type of firearm. It's a business permit, not a possession permit. There is no AW permit for simply collecting. You also have to meet a minimum requirement for secure storage of any weapons under the permit and must pass a DOJ inspection of the premisis to be permitted. An apartment with a nice Medeco deadbolt and ADT does not begin to meet the requirements. If you rent, you also need written permission from the owner to have AWs on the premisis. Assuming your place of residence or storage (whatever location you are trying to get a permit for) qualifies, you also must meet the "need" requirement which only allows permits to be issued to those who are engaged in the business of assault weapons and make sales/repairs to LE or gov't entities or do business with the entertainment industry. The permit also specifies transportation requirements for the AWs: Locked boxes inside you vehicle's trunk (the tunk itself does not count) and transporting the weapons only between places undewr the scope of the permit: movie locations, PDs, gov't client locations, generally ONLY locations that involve your business. Furthermore, even if issued, it does not allow you ANY activity beyond the scope of the permit: The permit does not allow you to go have a fun day out in the desert or at the range with your AWs. In a nutshell, the permit is the only way to import an AW into CA and the permit is only issued for doing legitimate business in the specific type of weapon.
Registered AWs are a different story, people who own registered AWs have some of the same requirements as permit holders, but not nearly as stringent. Handguns are a different matter. Any handgun (that is not also an AW) may be brought with you into CA, but you have to register all of them with DOJ. Not a big deal, it doesn't limit you in any way over buying it here. But the kicker here is you can bring with you ANY handgun, but what is available for sale here is limited to the DOJ approved list, meaning you'd be well-advised to check the list before you move here to see what is available for purchase in CA. ANy gun you want that is not on the list you'd better buy BEFORE coming here.