Start by unscrewing the solderless nipple. if it is really tight, use a pair of visegrips to stabilize the nipple body and use a bit of WD40 to free the nut. Once it is unscrewed, remove it completely from the cable and store it in a safe place.

Unsrew the Philips head screw in the handlebar assembly to free the lever from the bars (watch for washers). Once it is free, pull the cable until it is completely out of the outer tube. Grease the new cable down its entire length with large amounts of bearing grease (do it with gloves). Insert the new cable down the same hole the old one came out of. Push it bit by bit. There should be no snags. If there are snags in the cable, renew the outer cable as well.

Here is a picture of where my cable snapped. Hopefully, I won't have this happen again, given the amount of grease I used, but it is probably inevitable. I have been told cables have a life of about 6 months in everyday riding.

Here is a shot of some of the materials used in the job. Remember to always lubricate the cables. A big tub of bearing & chassis grease costs 5 bucks and will save big headaches in the future.

The inner cable will fall out of the other side. Loop the cable through the clucth arm and replace the nipple from earlier. Don't cut the cable yet. Tun the Slack Adjuster until it is all the way in.

Now yard on the end of the cable and pull until it seems tight, this will take up all the slack in the inner cable. once it seems tight, clamp the visegrips onto the cable so they rest on the slack adjuster. this will hold it tight while you fit the finnicky nipple. push the nipple right up against the clutch arm and tighten it, using another set of visegrips to stabilize the thing.

Now you will have to adjust the clutch. To do this turn the slack adjuster out (tighten it as shown) about half way. There is a fair bit of play in the clutch, so pulling it forward a bit should be okay. Get on the bike and start it -- in neutral of course. Put her into first (you may want a helmet). If it catwalks (does a wheelie), you have to tighten the slack adjuster. If it stalls after shifting into first, you are getting close. Keep tightening the adjuster until the bike runs smoothly after shifting into first. When you have finished calibrating the tension, cut the cable 3 inches or so from the nipple.