You make an initial assumption that you need experience to get hired. That is not a true statement. Plenty of companies hire new grads. And, they don't expect you to have experience at all.
So what do they want from a new grad? They want you to be smart. They want you to have natural talent for coding. That's basically it. If you have that, you're hired.
How do they determine that you're smart? The best measure of that is your GPA. You're pretty far along now, so hopefully you have a 3.5+ GPA, and failing that, you have a high GPA in your CS coursework. If you have the high GPA, put it on your resume. If you did any significant projects in school, put them on there as well.
Now, not all companies hire new grads. So, once you have your resume together, you need to find the companies that might hire you. One place is a career fair at your school. A second place is on linkedin. There are tons of recruiters on linkedin. Find them. Message them. Ask them if they're hiring for new grads. Hint: Larger companies are more likely than very small companies to do this. Also, get a linkedin account and link against everyone who is good in your CS program. You'll discover after you get hired someplace that companies pay $$ for engineering referrals. All those people you talk to in class every day can turn into serious coin in your pocket down the line.
Finally, you get some interviews. This is where they try to figure out if you have programming talent. The standard fare is data structures and whiteboard coding. Make sure you know data structures cold. Make sure you can code on a whiteboard. As in, "write a function that verifies a binary search tree is valid (in the sense that every node to the left is less than, and every node to the right is greater than)." Make sure you can do it well enough that the code (mostly) would compile. It doesn't have to be perfect, but it better not be 1/2 java, 1/4 pascal, and 1/4 random sloppy pseudocode. This takes practice to be good at. I suggest you spend time practicing with friends or you'll have a rough time your first few interviews.
Now, if you can do this, you WILL get offers. If you're in a big city, you'll probably get more than one. You don't realize it yet, but finding good programmers is hard. And companies snap them up (even new grads with no experience) when they find them.