Well I think it really depends on your area.
I had to take a very convoluted, difficult path get a spot at Boys' State.
I first found out about it when I was filling out the West Point SLS application/initial application. It sparked my curiosity so I decided to research. What I found about Boys' State really interested me so I asked my counseling office at my school if my school nominated people to Boys' State. They told me that they had never nominated anyone to Boys' State. So I just decided to email all of the local American Legion posts around me. One was about to give me a spot, but then they withdrew and the deadline to be selected passed. I was disheartened but I decided to keep emailing posts about possible openings. Eventually, I got one! The persistence paid off.
If you're a junior it might be too late (I know the registration deadline for California is approaching), but it can't hurt to try!
I never really answered your question though... It's very competitive. American legion posts nominate 1 or 2 boys from their local area (which could include 3 or 4 high schools!). I think they mostly look at class rank and ECs though.