1) your year in the program, (sophomore, junior, etc.);
2) what classes you have taken relevant to the research position (e.g. if you are interested in research in analytical chemistry, tell them how you did in analytical chemistry;
3) what your plans are in terms of a higher degree ("I hope to go to graduate school in chemistry" or "I am planning to be a medical doctor");
4) if applicable, a sentence describing prior research you have done.If you contact the faculty member by telephone first, ask them if they have a couple minutes now or if you should call back later (ask them what time is good), before you launch into a description of yourself.
In addition to the information above, they might be interested in knowing if one of the other faculty in the department know you well enough to vouch for you. The goal of a short email message or telephone call to faculty members is to set up an appointment to talk with the faculty member in person about research opportunities in their group. Telling them a bit about yourself during this call is up to you, but sometimes it helps a faculty member who is already over committed to research associates know if they should still meet with you.
When you go to the appointment to meet with the faculty member, they may ask you about yourself, your class work, and your interests, and they should tell you about what research opportunities there are in the current year or coming year in their group. In many groups you learn the most day to day from the undergraduate students in the group, so you may want to ask whether you will collaborate with an undergraduate student or work alone. If at the end of the conversation you are still enthusiastic and comfortable, ask the faculty member if they can take you on and how you should proceed (settle on what afternoons or evenings they can expect you to be in the laboratory, when group meetings are, etc.).
If you want to learn about opportunities in a couple more groups before actually asking a faculty member if you can work with them, let the faculty member know when you plan to contact them again and thank them for taking the time to let you know about possible research opportunities (do not take more than a week or two to look around once you have had serious conversations with one faculty member). It is most usual to approach your favorite person first so that if they spend a half hour telling you about their research and then tell you they have a spot available for you, you can tell them you are delighted to accept.
Do not get discouraged if your favorite group is already over committed so cannot offer you a position; this is often a first come-first serve situation so just ask their advice on what other research groups in the department they would recommend and go on to contact the other research groups that interest you).
Keep in mind that when you first work with a group it is a time to learn to be productive. If it is a good research project, it will take time to learn how to make a contribution.
You should not expect to be paid a salary during the academic year (although some faculty may do), but your work with the group during the academic year is very valuable in preparing you for a paid summer internship (many faculty members offer summer jobs first to students who have been working with them during the academic year, if things have gone well).