How will I find the parking in the Mission District neighborhood in San Francisco if I move there?

You can use Craig's List to find individuals renting out their spots. If you want a controlled-access garage it could cost $275-$350/month. The Mission Barlett garage charges $220/mo. for all times access, and slightly less for daytime only monthly parking.
As a permanent resident you can get an annual parking permit for the zone where your home is located for $109/year, or $54 if it expires within 6 months. The San Francisco Metropolitan Transportation agency issues permits that expire different times of the year depending on your zone. You'll need to go to their offices with a completed application and proof of residency (see their web site for more information).

I've lived in a home now without a garage for about 2 years. I've never really had much of an issue and I live near the commercial area that has more difficult parking restrictions. At most it takes me about 5 minutes to find a spot, and that is during the heaviest parking time. Most days I find parking with a minute or two and a block from my house.