Find an activity group focused around something you enjoy - there should be plenty on campus. If there's a public event that interests you, go, even if you go alone - even if you don't interact with anyone, it will give you practice engaging in a social setting and help with your anxiety.
One trick I've found is that people like it when you like them, and expressing a small compliment on a positive quality of theirs you note can often break the ice and signal that you'd like to be friends without being too forward. It also subtly expresses that you're confident enough that they will like you enough to care about your opinion.
Use small talk to start a conversation - simply remarking on something you're both observing is a start. "Nice weather we're having, ey?" is cliche as fuck, but it works. Angel the conversation towards points of agreement. Each point of agreement further enhances the ease of communication between the two of you.
Be willing to ask how others are doing, and be willing to listen. Most people aren't too choosy with casual friendships, and as long as they feel that you like them and are somewhat interesting to be around, they'll want to hang out with you.
Acceptance, sensitivity, positivity, confidence and loyalty are generally the traits folks value most in a friend. If you hit a couple of high notes in any of those categories, that's usually the start of a friendship if you have shared interests.
Good luck - if you've got anxiety, remember that the thought of going out and doing this is much worse than the actuality. Once you're out there, it will come naturally if you relax and let folks in.