I had to combine the responses I got to this point and add a few extra details so I'm answering my own question.
- Search for "Java developer" from Downloads for Apple Developers
- Download and install "Java for Mac OS X 10.6 Update 9 Developer Package" (or later).
- In IntelliJ, open File -> Project Structure.
- Click on "SDKs" under "Platform Settings".
Add the following paths under the "Documentation Paths" tab (the paths may be different based on which JDK you're using):
/Library/Java/JavaVirtualMachines/1.6.0_29-b11-402.jdk/Contents/Home/docs.jar!/docs/api
/Library/Java/JavaVirtualMachines/1.6.0_29-b11-402.jdk/Contents/Home/appledocs.jar!/appledoc/api
Add the following path under the Sourcepath tab:
/Library/Java/JavaVirtualMachines/1.6.0_29-b11-402.jdk/Contents/Home/src.jar!/src
Thanks, @Yishai for the download location and @Gareth Davis for the location of the documentation after installing.
Update for 10.7/10.8 [Mountain] Lion:
Steps are the same except for these changes:
In step 2, download "Java for OS X 2012-005 Developer Package" (or later).
Use these paths instead in step 5.
/Library/Java/JavaVirtualMachines/1.6.0_35-b10-428.jdk/Contents/Home/docs.jar!/docs/api
/Library/Java/JavaVirtualMachines/1.6.0_35-b10-428.jdk/Contents/Home/appledocs.jar!/appledoc/api
Use these paths instead in step 7.
/Library/Java/JavaVirtualMachines/1.6.0_35-b10-428.jdk/Contents/Home/src.jar!/src