For installing the Homebrew Channel, we recommend using ModMii. It’s a good tool, and you can get a guide generated with instructions.
SetMiiUp is also a good tool to get you started.
These tools require a PC running Windows.
However, these tools do not give instructions on how to install RiiConnect24 or Wiimmfi, so use the guide here to install those.
This guide is for the original Wii only, assuming you’re using the latest firmware. Do not use this on vWii (Wii Mode on a Wii U)! If you want to install homebrew on vWii, follow this tutorial.