Before you start, there are some tools you should have:
1. good quality screwdrivers that fit the rods and screws perfectly
2. a pair of smooth flat jaw pliers
3. a spring hook with both a hook and a notch end to pull or push springs
4. some quality key oil made for saxophones
5. some cotton pipe cleaners
6. some cotton buds (Q-Tips)
7. some paper towels
A good way to start would be to practice removing the single independent keys one at a time, cleaning and oiling them and putting them back on the sax. These are the palm keys, the side keys, and the fork F#. When you take off keys that have pivot screws on both ends, completely back one screw out and partially back out the other to prevent accidentally bending one. Keep these screws in the posts so they don't get mixed up. I always unhook the springs before removing keys to release the pressure on the rod so that it will slide out more easily.
When you are comfortable removing and installing the independent keys, you may want to try the upper stack. First unhook all of the springs with your spring hook. Back the rod out with the screw driver till it clicks on each turn. Grip the end with your fingertips and slowly pull it out. If you need to, use the smooth flat nose pliers to get it started. As each key is freed as the rod is removed, place it on a paper towel in the order it came off. This will be the reverse of the assembly order when you put them back on the sax. To oil keys, I like to put a drop or two inside the hinge tube at the end the rod will be inserted into. For pivot screws I like Music Medic Ultimax Lubricant.
A few general rules:
1. Never force a key on or off. Something will get bent. Figure out why it is not responding.
2. Always have a back up person you can take it to, if you get in over your head.
3. Have enough sense to know when you are getting in over your head and STOP.