If you are in a position where you don't have experience in your field because you are still a student, applying for internships is a great opportunity to get exposure in an industry you are interested in.
For references, first note that most internships do not have the same level of references required because the employer will typically take into account the student is not a seasoned professional. You can in these cases provide experience outside of work, such as volunteer work if a reference is asked for. Many internship candidates are selected because of potential and character, specific skill sets can be taught, candidate integrity and personalty cannot!
Great question! I had a difficult time finding references before applying to larger while in University. What really helped me was seeking out different employment opportunities not necessarily related to my final career goal.
While it may seem counter-intuitive to seek other opportunities outside of your ideal industry or sector, this will allow you to build diverse experiences, engage with different networks, and ultimately narrow down what you will want to do post university.
While on campus, I strongly encourage trying to join either industry related clubs or engage in volunteering. Visit your campus career center to seek out job openings posted on the university board, get advice on resumes. Furthermore, you should consider applying for jobs within your local/provincial/federal government. Often once you get in, you are able to transfer between different departments.
Don't be afraid to apply for an opportunity when it comes available even if it is not in your target area.
You can always build relationships with your professors to leverage their experiences and knowledge, learn about internship opportunities in their field and, if they're willing, you could use them as a reference to vouch for your character as it relates to their class.