Pretty much all clothing can be made to follow walking/running etc, though some full skirts may have problems with sitting poses. Essentially garments are rigged to follow the movement of bones in the figure they are fitted to (for instance the upper part of a pair of trousers will move with the right or left thigh of the figure).
As a default a conforming item (one with a ‘fit to’ option) should follow the movement of the character it is fitted to, but that doesn’t mean that it can only do that. It will also have its own rigging which will also allow you to move it independently of the underlying limb. Click on an item of clothing and you will see a similar set of joints listed to those of Genesis or any other character, these are the rigging.
But for a skirt the movement isn’t taken from simply one bone, and if you are trying to show the way it will swish around as someone stops or pivots, then it may not be following the bones of the character it is fitted to at all. The PAs who create clothing came up with several different ways to handle this, the two most common are
1) extra bones within the skirt. If you select a skirt rigged this way there will often be no thighs or whatever listed as a child of the hip and instead a set of bones shown below the hip, for instance left, left front, front, right front, right, right rear, rear, left rear. To make the skirt match a right leg forward pose you would move the right front bone until the skirt covered the leg, and then move the other bones until the skirt has a realistic flow to its fabric.
2) built in morphs. These are effectively extra hidden shapes for the garment, such as sitting or walking, presented on the parameter tab just like the options tthat allow you to change the shape of Genesis, and you may find morphs for things like ‘right leg forward’, or ‘sit’ and as you dial these in you will find the skirt moves towards that position.
Be aware that if you autofit clothing to Genesis with a version of Studio 4 prior to 4.5 it will not transfer morphs, and I believe it replaces any extra bones in a skirt with a default set, both of these may limit the ability of a skirt to easily follow a pose.
If you are having problems with a specific item of clothing, then if you let us know what it is, someone will probably be able to tell you how to deal with posing that item.