Hi.

To check if you are right on your diagnoses open the small access panel at the back of the dryer. You should be able to see the belt, the idler pulley and the motor. At this point unplug the dryer, do not attempt to work on it when it's powered up.
To replace the belt:
-remove the two phillips screws at the bottom (one in each corner) of the front panel, pull the bottom towards you and disengage top clips.
-next remove four 5/16 screws holding the front tumbler panel (don't take out the wrong screws there are more then four) and swing the panel to the left and secure it. This way you don't have to disconnect the wires.
-belt goes in with groves up (outside), align it on the drum over the old mark, make sure it's not falling into the grove on the drum behind the mark!
-use the rear access opening to install the belt, wrap it around the motor pulley and then over the idler pulley (large white pulley).
After you done with that, slowly turn the drum for a couple of turns to make sure it stays where it suppose to be. Check the idler pulley and make sure the blower wheel in front is not loose on the motor shaft, replace it if it's loose.

Here are the breakdown diagrams and parts list for you dryer

Model LDG8420AAW

Your belt Part number: AP4290988