Fastest way would be to come on a tourist visa, meet someone, decide to get married and apply for a change of status. If you go the fiance' route, you have to remain in your own country for some period of time before you can emigrate. The whole process is long, involved, and complicated though.

There is the H1-B visa route but you have to have skills such that an employer would sponsor you. These are more common in scientific fields like software and electrical engineering, biotech, etc. I've heard that some school districts have programs to hire teachers where they can get around the H1-B caps. I do not know if any NH districts do that.