Anyone. You do not even need to be a chemistry major. Likewise, chemistry majors can look for opportunities of interest outside of their home department.
Typically, we recommend beginning research your junior year. We also recommend that you plan to continue your research for at least one year. If you are able to continue beyond one year, then that is even better. It takes time to begin producing results that are productive. The longer you spend researching, the more opportunity you will have to gain useful results and possibly co-author publications on the results.
Research is a variable credit course. The rule of thumb is one credit corresponds to roughly four-five hours/week; two credits eight-10 hours/week. Your first semester in a lab, one credit is usually appropriate. You and your research mentor must agree upon the number of credits at the start of the semester. Most labs are quite flexible about when this work takes place, and your time should be scheduled in large enough blocks of time to actually complete some lab work while you are there. The schedule of the faculty member with whom you are working will also need to be considered when planning your work schedule.
Start by looking over the faculty research areas on our website. The faculty are listed with their division of chemistry and their research specialty. You can also look at faculty in other departments to see if their research matches your interest. Choose faculty whose work interests you, then talk to them. Face-to-face meetings are more effective than emails. Ask what kinds of projects students have been assigned in the past, what potential projects you might have, who would work with you as you learn the ropes, and how many hours you would be expected to work.
You will need departmental approval before you can register. And you will need to complete safety training before beginning work in the lab.
During the academic year, research is usually done for credit. However, during the summer, research typically is a paid position. There are a number of ways in which you can secure funding for the summer months: fellowships, internships, REU programs, or directly from faculty grants. Your chances of getting a paid position are always better if you have some existing research experience.
There are pros and cons to each option. It is difficult to be productive in research during the semester, so students who stay over the summer can make great progress that may lead to publication. On the flip side, research programs and internships done elsewhere allow you the opportunity to see and experience different areas of science and potential career paths and broaden your network. You should pursue the summer opportunities that are most appealing to you.