I want to know how to get my name in the hat for the election for State Rep. in Maine. I can't seem to find anything that is straight forward... Any help would be much appreciated.

You have to first get on the Democratic primary as running for that office. I'm not sure the specifics in Maine, but in other states you usually go to your county board of elections and register as a candidate for that office in the primary. Since primaries are around May, the deadlines can be as early as February. If you get in touch with your local Democratic chapter (county/city/whatever) they can give you more information, let you know your chances, etc.