Is Shadow Warrior: High Definition Wang free?

Yes. Shadow Warrior: High Definition Wang is released under Free fan mod (see the ModDB page for terms) and costs nothing. Neither it nor Shadow Warrior Classic Complete has any paid content.

What do I need to run Shadow Warrior: High Definition Wang?

Shadow Warrior Classic Complete, which is itself free. Shadow Warrior: High Definition Wang is an add-on and will not run standalone.

How do I install Shadow Warrior: High Definition Wang?

The PlayBound Launcher installs it in one click from Shadow Warrior Classic Complete's mods list. You can also install it by hand — full steps are on this page.