I'm a college student looking to approach people for the sake of overcoming approach anxiety. I'm starting off slow, just looking for friends, unless I find someone I like/click with. The best place for me to do this is the cafeteria. My question is how do I approach a group of people (guys and girls, or just girls)?

The other day I found a group I thought I would click with, and asked to join them. But I didn't really know how to make conversation and browsed my phone for a bit before trying to listen to key words in the conversation to join in. After recognizing that the atmosphere wasn't too friendly, I left. Was there anything I could've done better?