Of course you can do it on a Wii console. I bet that's what most people are doing.
You need the Homebrew channel and the Gecko code app (minimum).

ok so im just stupid.  i have those, and i've been doing texture and stage hacks, but i'm not understanding these directions.  where do the 3 files go?  i download the group so it contains a .raw, .wad, and .elf.

alright, i'm new to anything other than basic hacks, what is dolphin? is it a launcher like Gecko?  i use Gecko, where should i start?

Edit: I just did some research, is there a way to do this without dolphin? direct on a wii console.  or am i just stupid?