That is a rather curt description of your problem and task at hand.
I can safely presume you are talking about a Craftsman lathe, hence the reference to "101".
On to the carriage gears... If I go out on a limb and presume this is a 12" swing lathe (not the smaller 6" with which I have no experiance) then the following gears are "sweged" to their shafts:
Carriage Traverse gear 9-102-125 (Qty 2)
Cross-feed gears 9-102-24 (Qty 2)
There are all installed on the square ended shafts and then the end of the shaft is dimpled with a center punch very close to the edge such that the dimple upsets the metal and causes it to expand against the inside square hole in the gear.
I have successfully removed these gears from their shafts by supporting the gear on top of a stub of pipe (or open bench vise jaws) and driven the shaft out with a pin punch and ball-peen hammer. If the gear is worn, broken, or teeth stripped you don't care about any damage to the gear. I have done this several times without any damage to the gear.
To install a replacement gear on the same shaft file any burrs left from the previous center punch marks so a replacement can can be fitted - don't file too much, just enough top remove the burr. Once the gear is seated then lay it down on a anvil or other hard steel surface with the shaft vertical and using a center punch and hammer set several ding marks in the end of the shaft close to the square edges so that the gear is held fast.
Spiral_Chips