If you have arrived at the University with a teaching assistantship or a fellowship, you will be looking for an advisor. I cannot emphasize enough how important is the advisor to your graduation. You may be the most diligent and intelligent student, and still take years to graduate, because your advisor keeps on asking you to do 'one more thing' or does not approve of your ideas or is never around. Here are several pieces of advice to avoid this:

• Find someone that does research that interests you. Figure out which background you need for research in this field, and brush up on it before going to talk to your prospective advisor. They will be more impressed and likely to accept you.
• If you are uncertain what interests you take a few classes. You may also start working with different people, but let them know that you have not yet decided on doing Ph.D. work with them.
• The best way of approaching a prospective advisor is to take his/her class and do well. They will thus have some notion about your research potential and skills before they commit to being your advisor.
• Find someone that will be there for you. Ideally you would like to be able to meet your advisor at least once every two weeks and have a 1-hour chat about your research. If you find someone who is a famous researcher, always travels and has a thousandthings to do, chances are you will not receive enough attention. This is not always true. I have known great professors that have found time for advising amid frantic travels and engagements. Working for someone who is well known in the field has also a lot of advantages. They will have good ideas which problems are popular and worth working on. They will also have a lot of contacts to help you find an internship or a job. With their help, you may meet everyone worth knowing in the field. Just keep in mind to make sure they will work with you. Otherwise, you will see more hindrance than benefit from their being famous.
• Talk to the current students of your prospective advisor. Ask them how they like working with this person and how long in usually takes to graduate in this research group. Inquire whether they get enough help from their advisor and how they have chosen their research topic. Also inquire about funding. Does this advisor find support for his/her students or does he/she make them teach and do internships to support themselves through grad school.
• Talk to your prospective advisor about funding. Let them know whether you need it and when.

Short point summary

• Find someone that does interesting research
• Find someone that will be working with you
• Inform yourself as much as possible before commiting
• Let your prospective advisor know about your funding needs