I can't tell without the model #, but dryers that start making these sounds usually are beginning to experience a bearing failure. The other possibilty is debris in the air-channel or in the dryer cabinet.
Dryer drums are suspeneded in the cabinet in one of several ways. It may be on rollers, a rear drum spindle and bearing, or glides. Your description of the sound matches a spindle and bearing failure, but could be rollers. Both are fairly easy repairs but require the side or front of the dryer to be removed and the drum pulled out. As bad as that sounds, it is pretty easy if you take it one step at a time.
First thing is to use the model number and look at a diagram or parts list for your model on the Sears web-site
This will give you an idea of what part (rollers or bearing) you will need.