How to Find a Summer Internship (and Where to Find It)

You were about to reach the midpoint of your lecture when you looked at the window. It was a bright morning, probably a portent of good things to come this week. You were hoping that you could pass all your three examinations later this week. You were thinking of another miracle when you saw a strange object. You might still remember the first chapter of "Armada", Ernest Cline's second novel. It wouldn't be an Unidentified Flying Object (UFO), as your mind was drifting to other things. A summer internship was one of those things.
Your first year of college would come to an end very soon, and you've been thinking about internship. You wouldn't be too young for it, as there have been high school senior students who were looking for one. You weren't one of those students, as you led an easygoing life. There was nothing to be ashamed about it, as you told yourself that you should be looking into it in a year or two. You stuck to what you have said, insisting that there won't be a right age for it. And a personnel from the Careers Service confirmed it. (Many students would wait until their final year.)
The Careers Service should be the first place for queries. You encountered encouraging faces, prompting you to ask questions. It may not come to mind if they were the right questions, as you were going after valuable work experience. It won't be wise to put all your options here, though. Not that you won't be the best prospect, but there might be other ways. These options could turn out to be better (without disrespecting the valuable opinion of the friendly personnel from the Careers Service).
The first thing to ask yourself is why you want to be an intern. Money may put you off the list, even if your CV is impressive enough. If you're a student of the English Department, then consider the possibility of someone asking you about an academic career. It should be an option whether you admit it or not. How about authorship? A recruiter, if not someone from the company that you're applying for, can quiz you about it. And it can happen during that out-of-the-blue moment. The same thing applies to a B.S. Mathematics student, where there are more flexible options. Think of these possibilities when you compose your CV. This should lead you to that all-important step in the process.
Narrowing Your List of Options
LinkedIn. It's fine if you haven't visited this site, as your scouting for prospective companies (for internship) should lead you to this place. You may notice an important option, which is applying for a premium subscription. You may be too savvy for such a young age, which is a good thing. This would enable you to reach out to recruiters and/or employers, who aren't part of your networking circle. A monthly subscription of $30 may be too much for college students, but it won't be too heavy on your pocket if you make the most out of it. It means treating your account like it's not too different from Facebook (or Instagram). You can't post anything, as it should be related to your interests. And keep it as professional as possible.
Internship.com. Common sense would tell you that there should be a URL containing the very word that you've been thinking (or obsessing) for some time. There should be an opportunity for every state, but it may be impractical for a student from New England to send a CV to a company in remote Alaska. On the other hand, it's hard not to discount the possibility of working in sunny Florida. Proximity should be your basis for narrowing down your choices unless a company that is far from where you live may end up as your first job. And probably you're only one. Think about it.
CollegeRecruiter.com. Another website that you should guess from the very beginning, but be warned that you might have stiff competition. Current students and recent graduates are looking for internship opportunities, which would prompt you to consider creative methods of presenting your traits and/or skills on your CV. Different colors wouldn't notice you for the right reasons, though. It must point to your best traits, which could make you a valuable asset in any company. Always remember that this intern opportunity might be your first job.
To Pay or Not To Pay
If you're looking for experience, then you might be lucky to find an internship job in the shortest time. If you insist on being paid, then you have to do some digging. It could take you a while. There's nothing wrong in asking a recruiters/employers if you'll get paid (or not), but study their expressions when they answer your questions. If you sense that it won't do you any good during the next step(s), then look for other firms. And there won't be a limit to the number of companies that you're applying for.
Best of luck. And don't forget your coursework.