Here is the procedure I used to replace the harmonic balancer on my wife's 1998 Jeep Cherokee 4.0L engine.
1. Purchase harmonic balancer
2. Purchase puller tool
Here are pictures of the tool and new replacement part. I tried to make sure to get the part numbers (DA-242) in the shot.
Remove the old harmonic balancer
3. Remove metal splash guard/rock guard that protects the underside of the engine.
3a. Remove the three 13mm nuts
3b. Remove the two 15mm bolts
4. Put the car in 4th gear if you have a manual transmission. Chock the wheels for safety.
Here is a picture of the original harmonic balancer. You can clearly see the elastomer failed, as only the inner part is still attached to the car, and the elastomer looks torn along the diameter of the inner part.
5. Using a 19mm socket and breaker bar, remove the bolt and washer holding the harmonic balancer to the engine. Use a small bladed standard screwdriver to gently (gently!) pry off the center washer
6. Use the puller tool to remove the balancer from the crankshaft.
Install the new harmonic balancer
1. Place the balancer into the end of the crankshaft, and make sure the slot on the balancer is aligned with the key on the crankshaft.
2. Using a longer bolt of the same thread pitch and diameter of the bolt that held the harmonic balancer to the engine, or an installation tool, drive the balancer into the crankshaft.
3. Remove the tool
4. Install the correct washer and bolt.
5. Install the fan belt according to the correct routing diagram. On my car, it is a sticker on the fan guard
6. Install the splash guard/rock guard.