Use rail blocks at the top of the rails with appropriate chain falls attached. Remove oilers from each car top bracket (these brackets are designed for hanging car, just do 1 belt at a time and it wont be an issue) and install long reach clevis to each side. Land counterweight at a height that is comfortable for car top work. Pick car just enough to create slack on the belts. Drill small holes in ends of old and new belts and use seizing wire to "marriage" the belts (This is what EElevator and Rooster mentioned above) I also use wide gorilla tape about 8" above to 8 " below the marriage and keep it from coming apart.
Be very careful when pulling belts around so as to not get too much slack down at the counterweight. thats where it will get hung up and come apart of its gonna happen.
I've done alot of these over the past few years, so if you have any other questions, be sure let me know.
After the belting process is completed, the new belt data must be programmed into the LDU.