I know this has been addressed before, but I can't think of where or how recently. So here's a thumbnail.
Mickey's ToonTown Morning Madness (MTTMM) happens Mon, Wed, Fri. and Sat. Toontown normally opens to everybody one hour after the park opens. So if the park opens at 8 a.m., it opens at 9. On MTTMM days, it opens at 8 to those people holding special tickets for the event. You get the tickets when you book a package through Disney, Costco, AAA... that's all the ones I know of for sure, but might be other packages, too.
When you go, at opening of the park you head straight back for ToonTown. The CMs stand at the gates and collect your tickets. At around 25-30 minutes after the hour, when people have had time to get back there, they start a little show in the square in front of Toon Town city hall. The Fab 5 come out (Micky, Minnie, Goofy ,Donald and Daisy) plus a bunch of dancers etc and the Mayor of ToonTown. They do a song and dance about welcome to ToonTown, la la la etc. They do a little thing where they have a family of the day come up and get a plaque (Bumbershoot's family got picked for this... I still crack up when she tells about it, as soon as they asked where she was from and she said Tacoma, Washington, the sky opened up and it started to POUR

Washingtonians bring the rain with them!). Then Mickey is going to give a speech and forgets where he put his notes, gives it anyway off the cuff, the mayor declares you all are honorary members of ToonTown, they do the song and dance bit again, la la la... then all the characters rush off to their houses where they are immediately mobbed with huge lines for autographs and pictures. The whole little show takes maybe 15 minutes. It's cute. DD5 liked it but it was so packed, and everybody is standing, so it's hard for little kids to see over the crowd. DD10 thought it was lame, but that's just her. I could've easily given it a miss. Not that great, unless you are character fanatics, which we are not.
The only day it runs concurrently with Magic Morning is on Saturday. On that day, if park opening is at 8 a.m., then MM is at 7 a.m. In that case, ToonTown still opens at 8 a.m. for MTTMM.
Hope that helps!