Can I do research at a different college than the one I am attending? I will be general here so as to help others searching for the same question and to conceal my identity. 

I am a freshman at a top liberal arts college, and I would like to do chemistry research over the summer. I could pretty easily do research at my own college, but it is very far away from home and I'd like to at least spend my freshman summer closer to my family/friends back home. 

Would it be normal to contact professors at local colleges and say that I am interested in doing research over the summer? Is there a normal procedure (if any) in getting research opportunities at a college that I do not attend?
Thanks
There is nothing wrong with asking and nothing wrong with doing what you propose. However, your regular college may not accept any "credit toward graduation" from the other place, and the other college may require some sort of official attendance, even as a part-time student. 

Depending on how the professor is funded, this may be easier or harder. If he/she has external funding for the research it is probably easier as they have a bit (at least) more control over how it is carried out. Likewise if the professor is on an "academic year" contract then summer month activities may not be considered part of employment. But you will have to explore locally to know what rules apply. 

Your regular college won't have any problems with you doing this unless  you want them to accept credits. Then, rules will apply.