various high-school type jobs, nothing medical related
4 years active duty Marine infantryman; no medical training other than basic first aid stuff
I paid for a CNA class myself(~$400 and 6 weeks long)
I also took a phlebotomy (~$65 and two days long)
Then I applied for a job at a hospital(medsurg unit at a level 1 teaching hospital; about 400 beds) and got it.
Managers - Find out a way to contact the NMs on the floors you're interested in. Send them a copy of your resume and cover letter directly. Forget HR, at my hospital it's just a bunch of red tape for applicants and even employees. Even if there's no jobs posted, get the managers familiar with your name. They're the ones doing the hiring. Try to target the medsurg units as they tend to hire people with no experience. The ICU/ED/Surg etc usually require their techs to have hospital experience.
Volunteer - the volunteers we have do a lot of stuff for not getting paid. They pass out trays, get ice and water, transport pts for procedures, stock supplies, even help clean up pts. People get to know them and it provides a gateway to getting a job.
Students - At my hospital at least, they look for students to hire as techs. I don't know the official policy but it seems that the student techs are much more motivated than the "career" techs. Remember once you're hired as a tech, you're constantly building your resume to get hired on as an RN at that facility.
Sitting - Some patients require constant monitoring. So "sitters" just sit with the pt and make sure they don't pull out IVs, feeding tubes, get out of bed etc etc. It's a good way to get your face and name out there although not as well as volunteering since you're stuck in one room all shift but you're getting paid.