Choosing the best graduate internship means choosing an internship that most directly relates to one's field of study and, in particular, the one's niche within that field of study. Taking part in internships is a useful way to begin to learn the ins and outs of one's future professional field while also gaining on-the-job experience and making professional contacts. While an internship for an undergraduate may be less specific or geared towards a particular niche in a field, a graduate internship should be more focused, just as graduate studies are more focused than undergraduate studies.
Although some graduate internships are unpaid, it is quite possible to find a paid graduate internship. Many companies that offer internships to graduate students understand that the students are older than undergraduate students and have more financial responsibilities than undergraduate students. Furthermore, they are more experienced and can be more useful as members of the company, even if their time within the company is as short as one semester. Therefore, the ideal graduate internship is one that is both in the right niche of the right field and also offers at least a small stipend to compensate the student for her work.
Ideally, a graduate internship would be located in the student's city of residence. However, for graduate students attending schools that are located in rural areas or areas that are quite far from other cities, this might not be a possibility. In these cases, a summer graduate internship in another city might be a good choice. There are also some companies that offer online internships that are completed via telecommunication and involve regular phone conferences. These kinds of internships are great for graduate students who can't find the perfect graduate internship in their cities but want to complete internships while school is in session.
If at all possible, it is good for a student to look for graduate internship openings at companies that may have full-time positions open when the student finishes her degree. This is a situation that involves all of the stars aligning at the right time, but it is not an impossible scenario for a student who is looking at the big picture and considers a number of aspects when searching for internships. These kinds of internships are usually at large companies that have a chance of some turnover while the student is working there as an intern or at companies that are in a period of growth.