Q: How can I make a great impression in my internship this summer and land a full-time offer?
A: Build good working relationships with everyone, especially the hiring decision-makers. People hire people they like having around. Examples are to arrive early to meetings and use the time to create relationships, and attend all social events outside working hours.
Deliver results in your work, but most importantly, let people know about it. Prepare brief ‘soundbytes’ to deliver during 1-1 conversations and meetings, to publicize your accomplishments. You can also use soundbytes to publicize your previous work accomplishments or academic success, for example: “As part of my MBA I researched…” or, “When I led the marketing program at my former company, I learned that…”
Drop hints frequently that you would like to stay (don't be too subtle, especially if your hiring manager is a guy), and request an informational with your manager/the hiring manager to discuss this.
For more ideas on all the above buy The First 90 Days by Michael Watkins, about how to make the greatest impact in a new job.