First off, disclosure-
I know most of you may want evidence in the form of screenshots, but I will not tell you how to finish the MoM, that is the keynote in this thread because I have found there are a few different tactics you can use to make the whole experience more attune to how you decide to play around in the MoM, plus I also tend to not wear armor when soloing this quest as I find it restricting and noone and their mother would like to see any of my characters doing this deed naked...although I guess I could have worn a robe but hey call me a naturalist, although some may take the leather approach. Anyways this is the best take I can give those who wish a sort of guide to entering the MoM, and what to expect.
In soloing the MoM, I would suggest it is best to know the groundwork on how to get to the MoM so you can actually do the MoM. Noone tells you 'hey I want you to go out and do MoM and will offer a reward afterwards'. It doesn't work that way, you have no idea where the MoM is to begin with. I mean how are you supposed to enter the MoM if you can't figure out a locaction?? So I am going to do most of the dirty work for you here, as I have found finding the MoM is the hardest part of your mission.
Go to the Ruins of Gianthold, and in the lowermost Southwest corner of it you will find the MoM, but beware, there are some baddies who do not want you to get to the MoM, and will stop at nothing to prevent you from entering the MoM. But once you have found the MoM, enter the MoM ASAP as it provides a safe haven against those that may have chased you.
Once inside, you will be greeted by a Giant who seemed to have gotten stuck in the MoM. Things get weirder after that, and all else I can tell you is that if you don't hit the right switches the MoM can become a very unenjoyable experience for you. Eventually though you will get it right and finish the MoM and feel a sensation of 'YES I DID IT', smoke a cigarette afterwards if you smoke, or just sit back and relax and relish in your conquest. How you end it is entirely up to you.
Some people enjoy the Speed run with the MoM, while others like to it slow and easy when they are in the MoM, whatever floats your boat IMHO, I enjoy doing the MoM all sorts of different ways myself. Anyways, I would like to take a moment to thank those involved in hooking us up with the MoM, I'm sure it wasn't easy, but I thank you and look forward to some new quests kind of incorporating what I experienced in the MoM.
Hope this guide helps!!