I've created a brief show summary, which should catch even the newest of neophytes up on the show. Access it Here
If you want to learn about the characters in a brief, general way (without the in-deapth research or the fic-leaning information of the Character Profiles), click Here. If you're a sucker for punishment and want a short history on the Laverne and Shirley fandom itself, click Here.
A small list of links that should help you in your research.
Currently, the best episode guide for the series exists in the collection of archives, pushed over the top by user-contibuted information on individual episodes. Also worth noting is Epguides.com quick listing of episode titles. If you have the money, seasons 1, 2 and 3 are out on DVD in PAL conversions for all regions.
For general canon information, besides our own forums, you can always try out the LAS section of the Sitcoms Online Message Boards.
For general research into the 1950's and early to mid 1960's (that is, if you didn't actually live through the time), the best resources are Fiftiesweb.com and 1960sflashback.com. The former is especially good for date-specific music information.
If you want to cross over LAS characters with the folks from Happy Days or even Mork and Mindy, but haven't seen either show, here are a few URLs to help you out: