There is no law requiring a conversion. R-12 cannot be produced in or imported into this country, but existing stock may be sold to anyone holding a $20 EPA certificate (which also allows them to legally perform A/C work).
The operation of A/C systems is pretty standard, so normal trouble-shooting/service can be done by any competent shop. However, if major work is necessary, like tearing apart the dash, you probably want to have a tech experienced with your car perform the work.
Edit: There are good conversions and bad conversions. The good conversions replace every single seal and flex hose, and flush the entire system of old oil. The drier and fittings are replaced and, if necessary, the compressor is replaced with an updated unit. You can expect this procedure to cost quite a bit. Bad conversions remove the R-12, replace it with R-134a, add fitting adapters, and add some oil. This will work too-until the seals and hoses leak and/or the old and new chemicals interact to destroy the system. R-12 costs more, but unless you're replacing some faulty components already, usually better to stay with it. No matter what, R-134a won't cool as well as R-12.