I recommend you start by making sure the dryer is level. When the dryer is off balance, the vibration of it rocking even a little bit may cause parts to rub together and create a squeak. Lint build up inside the dryer can cause some squealing and squeaking of the dryer belt and pulleys.
Unplug the dryer and open up the cabinet (see the DIY guides below for a video showing you how to open your dryer). Manually turn the drum by hand and see if you can determine the source of the squealing. You could have a bad idler pulley or a support roller that is making the squealing noise.
You can find parts, diagrams, and your owner's manual on www.SearsPartsDirect.com
, just enter your full model number. If your full model number is 110.62332510, here is the parts listing: searspartsdirect.com/model/5li6i6nw6n-000582/kenmore-11062332510-dryer-parts
If your full model number is 110.62332511, here is the parts listing: searspartsdirect.com/model/5lhkrl5jz6-000582/kenmore-11062332511-dryer-parts
How to replace a dryer drum support roller DIY guide and video: searspartsdirect.com/diy/repair-guide/how-to-replace-a-dryer-drum-support-roller
How to replace a dryer idler pulley DIY guide and video: searspartsdirect.com/diy/repair-guide/how-to-replace-a-dryer-idler-pulley
If you do not feel confident repairing this problem yourself, then you can have it repaired at your home by a Sears technician by calling 1-800-4-MY-HOME.
Hope this helps!