It's kind of hard since most hospitals hire internally first, and a lot of CNAs learn they'd rather be a unit clerk so they get first crack. Also, most postings I've seen require at least a year of experience.
That said, I'm a unit clerk and have been on this job for 4 years. I went from applying online to setting up the interview in less than 48 hours. But I was also a monitor tech/ward clerk with 5 years experience prior to applying for this one, so my case may not be typical.
I originally got in the door with this gig through a hospital in my hometown. They offer classes in medical terminology
and EKG interpretation, both 12 weeks, and after finishing them, the instructor would sometimes make a recommendation to the managers and you could apply. Maybe call your local hospitals' HR or education departments and ask if they have anything like that.
For what it's worth, I like my job. I'm in the environment I like (ICU), I work full time, but only 3 days per week so it doesn't interfere with school that much (no personal life with class Mon-Fri and work Fri-Sun, but that's the sacrifice). The exposure is great: you learn a lot about the ordering process, labs, procedures, meds, computer systems etc. It's not as hands-on with the patients as being a CNA, but you get to learn more of the technical ins and outs. If you get a job at the hospital you want to work as an RN, you'll already know all the phone numbers, doctors, tube stations, computer shortcuts, supervisors, and more. I say go for it!