First, a disclaimer...
WARNING: THIS CAN/MAY BRICK YOUR WII IF USED INCORRECTLY; ONLY PROCEED IF YOU COMPLETELY UNDERSTAND THAT I DON'T TAKE ANY RESPONSIBLITY FOR WHAT HAPPENS TO YOUR WII AND THAT YOU FULLY UNDERSTAND WHAT THIS DOES AND HOW CARRY OUT THIS METHOD.
...next, what do we need? (Required for both Methods | Method 1 only | Method 2 only):
-Wii (with firmware 3.0-3.3v1; 3.3v2 and later will NOT work)*
-Method of loading Wii Homebrew (HBC, Twilight Hack, etc.)
-Access to MIOSv4 (see below for possible ways of getting this)
-Access to one of the following games (w/ MIOSv4)**: Pokemon Battle Revolution (U), Metroid Prime 3: Corruption (U), Big Brain Academy: Wii Degree (U)
-MIOSv4 from elsewhere (internet, etc.)***
*I'm not sure if the AnyTitle Deleter will work on 3.3 and above; it will work on 3.2 though.
**These are games listed on the Wiibrew Title Database, the other versions and different games MIGHT have MIOSv4, but they also may have a newer version instead. If you want to see if your game has MIOSv4, use WUFE to dump the updates from your disc to your SD card (you'll need roughly 200+mb free).
***The only risky thing here is that the MIOS file itself could be tampered with. With method 1, you know that the MIOS file is the original file from Nintendo.
Now we move on to the actual guide (it's a bit short, but I think I covered all I needed to; just ask if you have further questions). I highly recommend Method 1, which is probably the safest route out of the two. Just rent one of those games, or borrow them from a friend. You'll only need them once.
If you haven't already, run the Twilight Hack and install the Homebrew Channel. Next, download the AnyTitle Deleter from here. You'll be running this first. Now, run it and delete the copy of MIOS that is on your system. If for some reason you screw up later or can't install MIOSv4, you can always run Super Mario Galaxy, Super Smash Bros. Brawl, or Mario Kart Wii to install MIOSv5. Once you've completed this step, move on to Method 1 if you have those games, or go to Method 2 if you do not.
This is quite simple, just pop in one of those games with MIOSv4, run it from the disc channel (it should ask you to update, as you don't have any MIOS), and once it's done, you should be able to run the Old AR! Congrats!
This is a little more tricky/risky. I won't tell you where to get your MIOSv4 WAD nor will I tell you where to get WAD Manager; Google is your friend here. Once you have gotten both, create a directory in the root of your SD card called 'wad' and put your MIOSv4.wad file in there. Run the WAD Manager, install the MIOSv4 WAD, and it should (hopefully) install successfully. If it does, congrats, you can run the old AR.
If it didn't work (for whatever reason), just ask and I'll try to help you out. Oh, and before you ask, I do have a copy of MIOSv4, I will NOT upload it though. I am, however, seeing if I can find an alternative to Method 2. If you have any suggestions for improvements on the "mini"-guide, feel free to post them.
Oh, and stickied for justice.