If I have a file or directory that is a symbolic link and I commit it to a Git repository, what happens to it?
I would assume that it leaves it as a symbolic link until the file is deleted and then if you pull the file back from an old version it just creates a normal file.
What does it do when I delete the file it references? Does it just commit the dangling link?
From linux symlink manual (assuming you are in Linux):
A symbolic link is a special type of file whose contents are a string that is the pathname of another file, the file to which the link refers. (The contents of a symbolic link can be read using readlink(2).)
So a symbolic link is just another file, no different than a README.md or a Makefile. Git just stores the contents of the link (i.e. the aforementioned path of the file system object that it links to) in a 'blob' just like it would for any other file. It then stores the name, mode and type (including the fact that it is a symlink) in the tree object that represents its containing directory.
When you checkout a tree containing the link, it restores the object as a symlink regardless of whether the target file system object exists or not.
If you delete the file that the symlink references it doesn't affect the Git-controlled symlink in any way. You will have a dangling reference. It is up to the user to either remove or change the link to point to something valid if needed.