California Laws for Mopeds (Motorized Bicycles) are as follows
1. You need to register the moped withe DMV. Get the VIN and motor number (probably the same) and get form REG. 230 from the DMV. It is a 2 sided form. Use the side that says "Original Application for License". Send a check for $6 to the DMV in Sacramento(the address is on the form). DON'T take it to a local DMV, most of them don't understand the laws regarding mopeds.
This is a one time only Reg Fee and you don't have to renew each year. You can also request a new plate for $8.
2. You need at least a Class "C" vaild drivers license
3. you are supposed to have an "M2" license but most people don't bother but it is the law.
4. You must wear a helmet (motorcycle style, not bicycle)
5. no proof of insurnace is required but you can get Liability insurance for about $80 per year through AIS.
6. legal only on surface streets, no freeways
7. legal to ride in bike lanes
If you are in SF check with the city for their reqirements.
Some other tips on your Puch
I noticed it is a 2 speed, drain the tranny and refill with 9.5 ounces of ATF type "F" tranny fluid. DON'T top it off or overfill it. The tranny needs an air space.
Check the inside of the gas tank for rust. Treat it if it is really bad.
Flush the tank with kerosene or acetone until it looks clear.
You may have to get a new fuel petcock or remove and clean it.
Remove the carb and clean it.
Put in a new plug. I use NGK B5HS gapped at .018.
Clean the inside of the spark plug cap with electrical contact spray cleaner.
Gas/oil mix is 50:1 or 2.5 ounces to a gallon of regular gas. Ignore the stikcer that states "Do Not Use UnLeaded Gas". this a 1970s, 80s artifact.
Put it all back together and it should fire right up. You don't have to mess with the points and condensor unless it won't start after you have done all the above.