It's late for an answer but here it is, at least for future people looking for a solution on how to add the support library and resources for GridLayout (or ActionBarActivity / AppCompat, see below).
The easiest way is as follows.
Make sure you have installed the Android Support Library, from the Android SDK Manager.

In IDEA: Open your project, then select File / Import Module
- select the directory under the SDK:
{SDK}\extras\android\support\v7\gridlayout

- select
Import module from external model and Eclipse
- you can then select
Create module files near .classpath files, or choose to put them elsewhere if you can't / don't want to write into your SDK path
- in the next screen you should see
Select Eclipse projects to import and android-support-v7-gridlayout, IDEA will also ask you to reload the project.
- this should add a module
gridlayout [android-support-v7-gridlayout] in your project.
Now you have to update your project dependencies to this module for the resources, and add the .jar libraries. Select File / Project Structure
- select the
Modules project settings, and select your project (in the picture below, testv7)
- select the
Dependencies on the right panel
- add with the
+ button (on the right panel) a Module dependency... to the android-support-v7-gridlayout

- similarly, add a
Jars or directories... pointing to the {SDK}\extras\android\support\v7\gridlayout\libs directory (or to the .jar within). If you intend to use the v4 as well, choose {SDK}\extras\android\support\v7\appcompat\libs instead since it contains both v4 and v7 jars
- your settings should look like this:

And now you should be fine.
For me it was the only way out of the similar problem with the ActionBarActivity, which is solved using the same technique on the {SDK}\extras\android\support\v7\appcompat module. And I did try a few other ways ;)