Being a research intern at MSR is very different from being a software intern at Microsoft. I do not have any experience regarding the latter. But as a research intern, some of the tips would be - develop some diverse set of skills that can help you collaborate with other researchers, do some brainstorming sessions for potential projects, be actively involved in discussions, be productive in the 3 months of internship and maintain a good relationship with your mentor. However, very few research internships get converted to full-time offers and most of the times it a post-doc offer. In our batch last summer I know of one intern who was able to get a 2-year post-doc position offer after her internship. A lot depends on the needs of the lab for that year.
Since I had done this internship after first year of my PhD program, I wasn’t particularly looking for ways to turn into a full time job. But generally, I’d say, inform your manager a month or so into your internship that you’re interested in working there full time in future (given that you have built a positive relationship with your manager by then) and ask him to keep you in mind if an opportunity comes up in his team or a team he knows of. Try to reach out to other groups and network with them. Tell them about yourself and what you like doing. Learn about their work. Talk to the HR and ask them for directions for applying. Look at their open positions and approach the hiring managers for those positions.