On the other hand, you may have had inspiring teachers whose qualities make you seek them out to guide your research. You should plan to attend some of the regular meetings that most research groups have to get more of an insider's view of how that group works. You should also consider the style in directing research in selecting a research sponsor. Some individuals provide a great deal of direction and supervision which is especially useful when working in a complicated area with which you are just getting familiar but some may find restrictive. Others give you a great deal of freedom, nice when you work well in that setting but potentially frustrating if you don't.
Most students have little to show to convince a faculty member they can do a good job at research.
Sometimes students begin doing menial jobs such as dishwashing and then work their way into assisting in ongoing research before being able to get a research project of their own. The only general advice is to start looking early. By showing what you can do in simpler tasks you are more likely to be entrusted with work requiring more of your abilities. For another perspective on how to get started in research check the undergraduate research page. Bringing your Research Supervisor 'on board'.