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Every company has it's own criteria, and even these can vary depending on the type of internship that's available.
By and large the most common types of internships are "Summer Internships." Some companies and schools also partner up to offer internships during other months, so it can't hurt to ask.
The best place to start is to research the different companies that you want to intern with. A lot of times they will have a website with more information on job opportunities and internships specifically, if they're offered. If you don't see any information on their website, you can always look for a recruiter or contact to e-mail to ask for more information.
Getting an internship is similar to getting a job in the business world, it's infinitely easier through networking. Thus, talk to your professors and let them know you're interested in doing an internship, reach out to companies and let them know you're interested, find local events in your area and tell them you're a student looking to intern.