http://www.dmctalk.com/showthread.php?t=8699
The 2001 Chevy Cavalier automatic transmission shift linkage is held in place with a swivel nut on each end of the shift linkage. Turn the swivel nuts to the left and the shifting linkage will come off. Reverse the process to install your new shift linkage.
92 cavalier 31 clutch has to be on floor and still shifts hard
This depends on your experience with similar tasks and the wear on the linkage.
Replace shift linkage Replace shift linkage
To change the shift linkage in an 1998 automatic Chevy Cavalier the shift linkage needs to be removed from the transmission and pulled from the cabin. The job requires removing the floor console to access the cable. After doing the so the cable can be snaked from inside the cabin, the install is the reverse of the removal.
Bent shift linkage Frozen shifting linkage - try lubricating
The shift cable on an 01 Chevy Cavalier is replaced by removing the retaining screws, removing the cable from the shifter, and pulling it from the vehicle. A new cable can then be locked into place and bolted down.
All of the shift linkage should be internal. You will have to remove transmission, split the transmission in two to access the linkage.
http://www.gmpartscheap.com/seccat/cavalier-697/2003/shift-boot-41002/124/
Disconnect the linkage and reverse it. If is comes in from the top then turn it 180 degrees and replace it from the bottom with pin on top or vice versa.
It just pops off... Use a screwdriver to pry it off.
Remove the shift linkage and the bolts that hold the switch to the side of the transmission then rotate the switch while removing it from the shaft.