Several questions.

[ChaosWyrm]

1. How do I extract models from WC3?
2. What programs do I need to edit them?
3. How do I make a model for a skin to be attached to? (I need both the skin and the original model)

 

[Bankde]

This tool can answer all of your question. (Models from WC3 are stored in MPQ files in WCIII folders) You may also use MPQ Editor to extract models.

http://www.hiveworkshop.com/forums/tools-560/warcraft-iii-viewer-62878/

 

[Drunken_Jackal]

1. Use Warcraft 3 Veiwer select the War3x.mpq. And select the Extract MDX.
2. Edit them with War3 Model Editor
3. Use the original model used by the skin.

 

[GhostThruster]

2. Use Magos (as linked above) and MdlVis for animations (google it).
3. I recommend using GIMP to make skins, it is free and quite flexible.