What can I do since I’ve been here for 22 years without papers and wanting to join the military?

Go and speak to a military recruiter regarding your eligibility to enlist.

If you entered the U.S. before your 16th birthday, were under 31 on 7/15/2012, graduated from a high school (or have a GED), and have no criminal record, you can apply for a Deferred Action for Childhood Arrivals (DACA). Since this program was only recently implemented, no one can say for sure whether it will get you into the military; my guess is that it will not. But it would give you a work authorization and the ability to obtain a Social Security number and a driver's license. With these documents, you could visit a recruitment office and simply ask whether you can sign up.

From what I understand, the US military does not accept undocumented people to serve. But, if you have been here 22 years, you may qualify for other relief, and possibly a greencard, in which case you can apply to the military. How old are you? How old were you when you came to the US? Did you graduate high school or get a GED? Did you enter with or without permission? Have you ever left? Are you married to a citizen or resident? Has anyone ever applied for you before? Has anyone ever applied for your parents before?

If you are under 31 years of age and have graduated for high school or are currently in school, you can apply for deferred action under DACA and get a work permit for 2 years that can be renewed.