The chrome arm usually screws on to a threaded fitting behind the wall. If it's the chrome arm that broke, it should be easy to replace.
I'm guessing that you've got PVC pipe behind that wall, and it's a piece of PVC that broke. That stuff is not difficult to work with: hand tools and glue. Buy a book, or watch some videos. Definitely D-I-Y.
If it's copper, you'll have to use a torch, and learn how to solder. That's a tougher job, with a risk of fire.