Many larger companies have internship programs and even some smaller ones. Go to your school's career center to see if there are any companies that they are affiliated with. Also, look around at companies that are geographically close to where you are located, many look for local talent for internships and entry level positions.
Best of Luck!
Firstly, I would say that most jobs will help you build skills that will help you eventually pursue a career in engineering. All jobs, even if they don't seem related to engineering, will help you learn things like time management, responsibility, perseverance, and professional behavior. Additionally, whenever you leave any job, be sure to ask your colleagues and manager if they'd be willing to provide a reference in the future. That way, if a company you are interviewing with needs to know how you've done in past jobs, you have a list of supportive people you can give them to call.
To find internships, it's a great idea to visit your school's career center. They will have ideas for you or be able to refer you to other places to look for internships that fit your interests. For example, I now work in tech managing the internal process that helps our company run efficiently but I started out doing unrelated work--host in a restaurant, interning with a dance company in New York, and planning events for a nonprofit. Using what I had learned about how to be a good employee in the restaurant, I talked to my school's career center and they helped me get an internship on campus planning events for other students. Then I used that experience to get a full-time job at a nonprofit planning events and programs. Your career path doesn't need to be straight (and it might not be winding like mine) but all work can be useful experience in the early years of your career.
I'd also recommend researching some companies in your area and looking at the jobs page on their website. Sometimes, they might post internships right there on the site that you could apply for. A website like Indeed.com might also be a good place to look for an internship. They bring together thousands of companies who are looking for employees and interns. You set up a profile on Indeed and tell them what you're interested in doing then search away for internships or jobs that might be right for you.
Simone recommends the following next steps: