I believe there are some variations between different cities, as well. So I would check with your local authorities near your residence.
For me, I had to go to the local city PD and sign up for a purchase permit. What happens then is they do a background check. If you have no criminal record, they say it takes 24 hours, if you do, it takes 48 hours. Then you go back and pick up your purchase permit. The permit where I live is good for 10 days. If you find a gun you want 11 days later, then you have to get another purchase permit.
I bought my gun from out of state, so I took my purchase permit to my FFL (who had received the shipped gun). He filled out all the necessary stuff. Then I had to take the gun back to the local PD for them to record the serial number, capacity, caliber, model, etc. They never test fired it or anything like that. It took all of 10 minutes. Then they gave me a little card that is basically a copy of my registration proving that I own the gun. Then I walked out with my gun.
So all in all, it took me about 2-3 days to get my gun from the time it came in, but the extra day was b/c I couldn't get off work 24 hours after my background check during city hours. Longer than it should be, but do-able. I think this whole purchase permit & registration business is a bunch of unconstitutional garbage, but that's me. There are states that are worse off, though that's no excuse for violating the constitution.
Regarding FFL transfers... check with your local PD as to the length of validity of purchase permits. Ours is 10 days. So I contacted the guy whose gun I wanted, negotiated a price, contacted my FFL (who contacted the seller), sent the seller my check, and then he shipped it to my FFL. Once I got confirmation that it had been sent and was en route, I then got my purchase permit (figuring it'd take a few days to get to the FFL, but not more than 10). It took about 3-4 days shipping. Then I brought my purchase permit to the FFL, went back to the PD to register the gun, and then I was done.