i spent many years doing research, here's how i got involved (or some advice)
at the med school i worked in, most people started early. there were forms to fill out, and stipends, some programs even based on GPA. so fyi, may or march is the time to start looking ...
the other thing would be to ask profs at your school, if you haven't already...there must be some research going on, unless you're home away from your school..
because of grant issues, most places wont just take someone without pay. you also can't work in a lab with out some physical /tb tests or lab safety requirements. these things take time, which is why they may be lax to take someone on later in the year.
yeah, most people know Phd's and PI's personally. i've seen PI's family members work on projects. most of the lab experience however is delegated to tech type stuff that are given to high school students or something.
with all this in mind:
your best bet is to physically go to the place you want to do research. not everyone reads emails or what have you. ask human resources what opportunities they have for med students.
you could also find the PI you want to work with, go there and talk to the secretary. they may be able to schedule an appointment for you, and then you can state your case. especially if you have some lab skills (PCR, western blot, etc) find a PI that has a huge lab--the biggest labs always need people to do things..
keep in mind though that one summer of research won't do much to help you--you want to have some kind of consistent research where you (hopefully, ) at least get mentioned on a paper. not everything you may do will even go into a paper, and rarely do students get to co -author one (which is where research really counts).
if you are itching to do something, your last bet would be to volunteer in some kind of "street medicine" or community outreach that's health related (i.e aids clinic, mental health crisis center, etc)
hope this helps, and good luck