I went to Boys' State of Kansas last year, and my best advice would just be to get out there and run for what you want to. Also, this might be fairly obvious, but if you want to get to know a few people really well, try to get something on the county or even city level. It seemed to me that the guys that did that got really close to the people they were around because they were with them for most of the camp. If you want to meet more people, run for something on the state level. Even if you are unsuccessful (like I was, for the most part) you will meet lots of people.
Also, I don't know if you guys will have some huge debate before the elections for all of the state offices, but if it was like my year at Boys' State, that debate is the most critical thing to success after nominations are made. I was supporting a candidate for governor who everyone was sure would win because he was so popular, but after he pretty much choked in the debate, they elected the other guy. If it's like my year where they give you the questions in advance, you should definitely have good answers prepared. The parties seemed to be set up so that each one was generally conservative or liberal, but people were fairly willing to vote across party lines if one candidate was clearly better than the other.
As for getting the nomination in the first place... well, I was unsuccessful, but I would say that the best thing would be to just get your name out there. If you have some kind of party meeting (where people mainly work on the platform, etc.), definitely get involved in that. If your Boys' State has a newspaper, utilize that. If you have some type of whistle-stop tour, utilize that. Meeting lots of people and having a good personality are also important things. It's sort of difficult to stand out among all of the guys running for the same position, but if people are talking about you and you have some momentum (I guess sort of like real elections), you will have a better chance at success during nominations. If you seem popular, people will back you. If you're successful in all of that and win the nomination, people will have pretty high expectations. So then, like I said before, rising to the occasion during the major debate seemed to be by far the most important factor in the general election.
Good luck and I hope you have a great time!