First, let me help with your terminology.

The bottom portion where your wheel attaches, is painted and has the reverse arch that connects the two sides is called your "Sliders".

The sliders, slide on the "Stanctions" the smooth metal thingies.

The insides of the stanctions are your "internals" and depending on your model will have a variety of stuff in them. Damping cartridges, compression cartridges, springs, oil, air...etc.

The stanctions connect to the "crown". Most forks nowadays have the stanctions pressed fit into the crown.

The single tube going out the top of the crown that goes through the frame and is held together by the stem is called the "Steerer Tube".

The Sliders slide on the stanctions are have rubber seals on them. It's a good idea to lightly lube these rubber seals. Any lightweight lube will work. Tri-Flow or Pedro's Dry lube, or even that household 3-in-1 stuff. Just a little. You just want to keep the seals moistened.

Again depending on your model, you may have an oil fork. You would have to remove the top caps on either side of the fork crown to inspect. But that's another story!