I need step by step instructions on how to replace the throttle cable on a 1980 harley sportster

Ok, you should have two cables on your Sportster. One is the throttle cable that pulls the carb open and the other is the idle cable that acts as "safety cable" to pull the carb closed should the throttle return spring on the carb break.

To replace either or both of the cables, it will be easier to remove the fuel tank before doing so. Make sure you look at how the cable are routed from your handlebar grip to the carb. Drain the fuel and take the tank off your bike.

Now, first loosen the cable adjusters so that you have all the slack you can get in the cables. Take the two bolts out that hold the right hand switch housing halves together. Carefully lift the top half off exposing the nylon throttle sleeve. The cables are connect so that the throttle cable is to the front and the idle cable is to the rear. Work one cable at a time out of the sleeve. Be careful and do not loose the "barrel" that goes on each cable. With the cables out of the throttle sleeve, you can pull them down through the throttle housing. Then, disconnect the cables at the carb.

To reinstall the cables, do everything in reverse. Make sure you pull the throttle grip off the handlebars and apply a bit of white lithium grease to the handlebar, inside the throttle grip, and on the nylon throttle sleeve where the cables connect. Get everything assembled but just before you tighten the bolts that hold the switch housings together, slide the throttle assembly towards the center of the handlebars until it stops, then back if off about a 1/4 or 3/8 inch. Do not adjust the throttle or idle cables too tightly, you need just a bit of slack in each one or the throttle will hang. When you think you're finished, with the engine off, turn the throttle to the wide open position and release it. It should snap back to the fully closed position. If not, work with it until you get it where it does. Reinstall the fuel tank.

Caution, failure to insure proper throttle operation could cause serious injury or death. Do the job right or take it to someone that can. Your health or your life ain't worth risking for the few bucks you save.

Ride Safe
Steve