Internship is a form of employment for students. As a F-1 student, you are eligible for internship after you have been a full-time student in the US for at least 9 months. 

Many companies have internship programs. Some government agencies also have it (for international students  the World Bank is especially attractive). 

Contact people in your area, or even the career center of your school for internship opportunities. 

For F-1 students, internship has to be in the form of a practical training. You have two practical training: curricular practical training (CPT) and optional practical training (OPT). You have a  total of 12 months for each. The best strategy is for you to take OPT after your graduate and before you get a work visa (H1), considering that fact that it may up to five month for you to get H1 visa. OPT cannot start over two months after your graduation. Therefore you should use your CPT quota for internship first.

For you to be approved for internship with CPT, you need to get approval from your program or your advisor, showing that the internship is related to your program. Then you need to go to the international students office to get their approval. They will put something on your I-20 form showing that you are authorized to work at  that place for that period of time (as shown on your offer letter). You will also need to register for a class for at least 1 credit for this internship, which means you need to pay tuition for it.