Seems to be a lot of transmission failures among the line of the Saturn Vue. This how-to was based on a 2002-2007 Saturn Vue with the 2.2L engine and AWD DEX CVT (continuously variable transmission) transmission.
Start by removing the front wheels.
Remove the battery and battery cradle.
Here is the battery box removed:
Remove the support bracket under the battery support box.
Unplug the 2 electrical connectors on the transmission.
Disconnect the shift linkage.
Tie up the radiator and ac condenser to hold them up and in place.
Support the driver side of the engine with a shop crane aka cherry picker.
Unbolt the sway bar and steering rack and pinion on both sides.
Remove the front axles and disconnect the rear driveshaft.. A detailed write up of removing the front axles can be found here: http://diysrc.com/remove-and-replace-front-cv-axles-saturn-vue-awd/
Disconnect and drain the transmission cooler lines.
Unbolt the lower transmission mounting brackets.
Support the engine cradle with adjustable hydraulic jacks.
Remove the bolts holding the engine cradle.
Lower the engine cradle and remove it from the work area.
Unbolt the starter. Remove the bolts from the starter opening on the flywheel. You must rotate the engine to access all of them.
Unbolt the top transmission support, transmission bolts and remove the transmission to finish the job.
Time to find a donor transmission