Here's the procedure for rotating tires recommended by the book "Auto Upkeep - Basic Car Care":
Put on your safety glasses.
Check the owner?s manual for recommended tire rotation patterns.
Remove wheel covers if applicable. Check the owner?s manual for procedure. Some covers (hubcaps) have locking mechanisms that need to be removed first.
Loosen lug nuts one complete turn with a lug wrench, but no further.
[The Camry manual says to loosen one-half turn (not much of a difference.)]
Use jack and jack stands (or an automotive lift) to raise and support the vehicle.
Note the position of each tire.
Remove the lug nuts on each tire.
Remove each tire and move it to the new location according to the owner?s manual recommendations.
Apply anti-seize compound to the wheel stud threads.
[Built_Well's note: The above step sounds counter-intuitive to me. The manual says not to put oil or grease on the wheel's nuts and bolts because it can result in over-tightening with a wrench, and also result in the nuts loosening over time. I believe "wheel stud threads" refers to the wheel's bolts, and you screw the lug nuts onto the bolts. So it doesn't sound right to put anti-seize here. Maybe putting anti-seize on the hub and wheel mounting surfaces is okay, like Ray says, but on the bolts?!]
[Here's the exact wording from the manual: "Caution. Never use oil or grease on the bolts or nuts. The nuts may loosen and the wheels may fall off, which could cause a serious accident."]
Start all lug nuts by hand. Do not cross-thread nuts.
Spin the nuts on with a lug wrench and snug. Use a star pattern when tightening lug nuts.
[The manual says to "reinstall all the wheel nuts finger-tight" while the car is in the air.]
Do not use a pneumatic wrench at this time.
Lower the vehicle /just/ until the tires touch the ground.
[Why not lower the car completely at this point, as recommended by the Camry manual?]
Check the owner?s manual or specification?s chart for torque recommendations.
Use a torque wrench or color-coded torque sticks with an impact wrench to tighten the lug nuts on each wheel. When tightening, use a star pattern.
Failure to torque wheels may result in warped brake rotors. Under-torqued wheels may allow the wheel to work loose and come off when driving, causing a hazardous situation.
Completely lower the vehicle.
Recheck all lug nuts with the torque wrench.
Replace wheel covers.
Clean and put away all tools.