** I can set the dial to a time, yet when it is time or it to shut off, it doesn't. **
If the timer doesn't move at all in the timed setting, I agree the problem is most likely in the timer which will usually need to be replaced. It is often not too difficult of job to accomplish on a dryer.
If the timer doesn't advance in the "auto" or "Permanent press" cycle, it could be a problem in one of the controls. Posting the model number off the dryer would help in this case. (You can find tips for locating the model number on your appliances in the 'Repair Part' section of my site link below.)
If the timer advances right past the "off" position and just keeps going, that could be caused by a shorted heater element or on some models, a defective motor switch.
In any event, clarifying exactly what the problem is and which cycle it happens on would help us to provide you possible causes and courses of action.