This assumes that you have a basic Kenmore / Whirlpool top load, direct drive, neutral drain (it doesn't spin until the pump removes most of the water) machine.
First, see the Sears parts site for your washer:
http://www.searspartsdirect.com/partsdirect/index.action
Enter your model number (###.######) and you'll see a list of major sub-components with diagrams and parts.
Look at the section on the Sears site for Agitator, basket and tub.
Assuming that only the top section of the agitator is "slipping, the problem points to the Agitator "Dogs"
See the following for how to replace them.
http://www.american-appliance.com/catalog/newsdesk_info.php?newsPath=16&newsdesk_id=136&osCsid=8878c06f855a89c90959d53553cf9ab8
If it's not the "Dogs" see the following that has a section on how to remove the agitators and check the splines.
http://www.american-appliance.com/catalog/newsdesk_info.php?newsPath=16&newsdesk_id=137
This is usually the agitator dogs have worn out or broke. These are very inexpensive and easy to replace. Here is a video this will walk you thru checking and replacing the agitator dogs . You can also enter your model # for diagrams and illustrations of your specific model. Not all models are available. All parts come with installation instructions.
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