I was an international student as well while I was in college and there are many ways to think through the internship process. The first step is to speak to your international students office in college. This would be the most helpful first step so go for that. Secondly, reach out to the career center at your school. The career center normally knows which internships are open to international students. Below is a link to information for students on F-1 visas:
Be confident in yourself. Getting a first internship can be hard especially when you have no experience. Some experiences are valid such as sports, extracurricular activities or campus jobs. If you don't get an internship opportunity, I would encourage you to volunteer or take a course online to build up skills or experience.
My first summer I volunteered at a non-profit. My second summer I spoke to my career center and the international student center where they showed me available internship opportunities. One I got an internship offer, I applied for CPT (Curricular Practical Training) which is what international students use as work authorization. This is something done with your school. Next step will be going to work. Hope this helps. I wish you all the best.