There are new horses who just moved in next door and the really nice man is letting me ride his horses, I came on here mostly because I'm bored.
What do I do first? Should I get to know them before I ride and what are some things to settle down my nervousness?
I would just start spending time with them. Go out and just hang out with the horses, maybe groom them. Let them get to know who you are. Eventually you won't be nervous around them or at the barn in general. By the time you start riding them you shouldn't be nervous. Just take it slow when you first ride, establish yourself. :)