How do you increase your rank in the us military?

It really depends on the branch of service mainly because each branch has its own regulations and procedures on promotion's, however one way would be:

Increase or strengthen yourself physically
Consider taking college courses
Request additional duties
Know everything there is to know about you MOS (job)
Know your current role and at the least 2 ranks ahead of you
Know all the programs that the branch offers

Basically improve yourself by improving your organization and request additional responsibilities showing that you are ready for that next rank.