Setting up active directory integration in SharePoint 2013 can be extremely simple.
If you only need to import users, and not write back changes to AD, the User Profile (UP) service is a good alternative to the User Profile Synchronization (UPS) service.
The short version if you know where to go:
1.Check that the UP service is running, and if necessary, create a UPA (User service profile application)
2.CA\Manage Profile Service\Configure Synchronization Settings: Select "Use SharePoint Active Directory Import" under synchronization settings
3.CA\Manage Profile Service\Configure Synchronization connections - add new connection
4.Fill in the data and click "Populate Containers" to verify. This is the crucial part. If correct, you will see the AD tree. Select one or more groups/users and click ok
5.CA\Manage Profile Service\Configure Synchronization Timer job: edit your schedule if necessary, and "Run now" if you are eager to get it done
You can examine ULS logs to get a closer look on what is happening or if you run into problems. If not, you should be done, and your AD users should be available in SharePoint! :)