A typical Kenmore dryer is a fairly simple machine. Parts are usually available from Sears and not expensive. Probably the most costlly are the motor and the timer switch. Things like belts or the centre drum bearing are usually a very reasonable cost.
Required are: Basic mechanical repair skills? Tools? Electrical circuit knowledge? Some sort of test lamp or test meter.
A dryer basically does 6 things. It rotates the drum. It blows air. It heats the air. It has a timer switch which you set to the running time; it then shuts off the machine. It has a thermostat that controls the temperature of the heated air. It has some safety overheat switches and a door switch. There is a wiring circuit that connects it all together. Most Kenmore dryers I have seen use just the 230 volts to operate all electrical functions.
If you are lucky there MAY be a circuit diagram on or inside the back panel; or maybe not.
The simplest fault we have encountered has been a broken belt that prevented the drum from rotating. In another instance a spring costing $3.50 broke and while belt was not broken belt was not tensioned and drum did not turn. Aonther fault was the dry bearing of the blower impeller'. It stuck and the belt driving it was slipping, burning and became damaged. The most extensive and potentially most costly problem has been burnt out contacts within the motor. These contacts completed the heater circuit so while the motor would run and drum would rotate the heating circuit did not operate. Such a motor is expensive. We were able to add a relay that overcame the problem without replacing the motor. Another fault with either our dryer or washer (can't remember which!) was a defective contact inside the timer switch. Potentially somewhat expensive but we were able to either repair it or substitute a complete timer with parts from a machine scrapped by another member of the family!
Our dryer is now 42 years old. It has has been repaired about six times; only twice has it been a major problem. We are estimating that with another belt or something minor it will probably last 50.
Some years ago somebody gave us another Kenmore which we fixed with one spring. A couple of years after that we gave it to an acquaintance; she returned it "because it wasn't blowing air" recently. We found that the blower impeller belt was broken because the blower had been jammed by a piece of springy metal from a bra! (Size 'D' by the look of it!).
Hope these suggstions may help you keep abreast of your problem!
Terry.