Hello,
Welcome to
FixYa.
It sounds to me what you're describing is worn brake pads on your washer's
gearcase, thus not holding the basket while the unit agitates. It is actually fairly common and regular wear over time.
You can purchase the pads at most brick & mortar appliance parts depots or on-line parts vendors such as "repairclinic.com" or "searspartsdirect.com" to name a couple for around $20USD.
**Unplug the washer from the wall before performing any service...safety first**
If you pull the front panel of the washer off and look at the bottom of the transmission...above the belt pulley you should see three carbon pads as these shown here...
Everything in the image is included in the kit as well as instructions to install them. If you follow this link you can observe an exploded illustration of the components I'm referring to as well...
http://www.searspartsdirect.com/partsdirect/partsdirect/showSubComp.pd?imageUrl=http%3a%2f%2fc.searspartsdirect.com%2flis_png%2fPLDM%2fI2204660-00013.png
Installing the new pads is actually really straight forward and requires only removing the old ones, and it isn't too difficult with a little patience and a small socket set.
Hope this helps move you forward. Let me know if I can assist you further and I will try and help in any manner I can. Good luck.
Regards,
Macmarkus :)