Getting your first internship with no experience feels like a chicken and egg problem, because you need experience to get experience, but there are clear ways through it, and everyone who has an impressive resume started exactly where you are now. The key is to show potential, effort, and relevant skills, since employers offering internships usually expect you to be learning, not already expert.
First, build something to show even without a job. Do small personal projects, take online courses and earn certificates, volunteer, help a club or a local business, or create sample work in your field of interest. This gives you something concrete to point to, which matters far more than the word experience. A student applying for a design internship with a few practice designs, or a marketing internship with a small page they grew, instantly stands out from someone with nothing to show.
Second, cast a wide, active net. Apply to many internships including at small companies and startups, which are often more open to beginners, and do not only wait for listings. Reach out directly and politely to companies, professors, and people in your field, because a lot of early opportunities come from simply asking. Make a clean resume that highlights your skills, projects, and willingness to learn rather than pretending to have experience you lack. Tailor each application, write a short genuine message about why you are interested, and follow up. Rejections are normal and not personal, so keep applying. Your first internship is the hardest to get, and once you have any experience, the next ones come far more easily.
Example: A student with no formal experience who shows two self made projects and emails ten small companies directly will usually land an internship faster than one who only submits a blank resume to big listings.
One practical tip: Create your own proof of skill through projects and courses, then apply widely and reach out directly. Shown potential beats a blank resume every time.