Is HoMM3 HD Mod free?

Yes. HoMM3 HD Mod is released under Open Source / Community and costs nothing. Neither it nor Heroes of Might and Magic III: Complete has any paid content.

What do I need to run HoMM3 HD Mod?

Heroes of Might and Magic III: Complete, which is itself free. HoMM3 HD Mod is an add-on and will not run standalone.

How do I install HoMM3 HD Mod?

The PlayBound Launcher installs it in one click from Heroes of Might and Magic III: Complete's mods list. You can also install it by hand — full steps are on this page.