Someone posted this picture of an ignition switch so I thought I would use it to show first of all what the 2000 era switches are like inside. The switch block is held onto the key part by 2 Phillips screws, it takes just a few seconds to drop off.
Release the clip on the black body and tilt the white switch plate out.
In this one the grease looks quite fresh, often its hard almost like candle wax. Wipe the old grease out and replace it with fresh Vaseline.
Note how the green wire has snapped off, it did that because the wires aren't held at the back so they flex at the weakest part, next to the solder joint until the copper work hardens and snaps.
I don't think it is possible to put the switch together wrong, at least I haven't managed to yet.
When you put it back together, fasten the wires to the back cover and arrange them so the loom flexes gently over several inches, don't strap the wires tightly together.