Using "connections" to get a job

I'll start off by saying I am not a nurse yet, I am still doing my pre-nursing classes. I have a B.A. from 2007 but I have only worked part time, with a gap in my in my history due to being a stay-at -home parent and having 2 kids in two years. The last job I left in the spring, I won't go into why (not fired) I am trying to find a tech job to keep my work history current and bc I keep hearing that if you get one, you are all but guaranteed to be hired on later as a nurse.

I have applied to several places online, and haven't heard back. I decided I need to step up my search and started trying to network. I emailed all the recruitment managers at local hospitals. I volunteer at a hosp. right now, so I was thinking of asking the team leader where I volunteer if she could set me up with a recruiter. I don't know her well, so I've been waiting until I have some more time volunteering and the nurses know me better. I also chatted up a girl yesterday in my Chem class who is a tech at a local hospital. I keep hearing that it helps to know someone on the "inside" but I am not sure exactly what to ask that will help lend a job. If you know someone who works in the hospital, how exactly does that help you? Should I ask if they are looking for people on her floor?

Also, what questions should I ask at the place I volunteer? I wanted to talk to the team leader next week when I go in, and ask if there is she could maybe recommend me for any unit that uses techs (I know the unit where I volunteer doesn't). Just not sure how to have that conversation professionally, so if you have any pointers, that would really help.