Earlier quoted context omitted.
Yes, we hire new grads, and we offer internships for those who are still studying. Successful interns get an easier path for converting to full-time than grads who apply cold. Getting somebody you know at Google to refer you is the best way to secure an interview, but you can also apply online. http://www.google.com/about/careers/students/
Well that's too bad, I don't know any people at google. I guess I need to hang around more coffee shops.
The hiring process is a bit hit and miss. I know people who had a really good experience, and I know people who said it was a shit show. About meeting Googlers: if you happen to come to the Bay Area, you can't throw a rock in any direction without hitting at least one Googler. Not saying throwing rocks is the way to go, but... you'll get someone's attention :P