I have a number of project demos which are already in Git. I expected that Intellij would just pick up on this fact... and it did not. I then created a new project, did a Git init from Intellij and all was good.
To get IDEA to recognize a project already in Git, under the Version Control menu, select Enable Version Control Integration, then Git.
So far... the Git integration is fantastic!!! Love it! Well done JetBrains!