Google rarely makes full-time offers after an internship because they want you to finish your school first. My recommendation is to become a repeat intern if possible. during your internship(s), show initiative and eagerness to learn. Be a team player. When you graduate, apply for their IT Residency Program. Another important thing is to be willing to relocate.
One way to view an internship is as a "super interview." Unless things have changed recently, you can attempt to "convert" to full-time at the end of your internship, in which case they'll set up practice interviews for you. Eventually you'll have an interview that forms a part of your application; however, my understanding is that your internship performance is viewed as an even larger factor in the hiring process, not least because it provides a sample of how you work on an actual project over time and in collaboration with real Googlers. Furthermore, I think that Google views strong interns as very desirable candidates because both sides come into the conversion with a good idea of what to expect.
Since I am a sophomore, I received a returning internship offer rather than a full-time offer. One of the things you can do is to be efficient with your time and with the time of others. That means showing up to meetings prepared (I usually came with a written agenda and some questions I wanted to ask) in addition to spending your working time wisely. For instance, I usually had a working list of things I wanted to accomplish, and while code was being tested, I would start working on the next item.