Megaminx
The Megaminx a puzzle with 12 faces is not much harder to solve than a 3x3, probably if you can solve a 3x3 you should be able to get at least the whole megaminx besides the Last Layer. Here I show you my method with which I'm quite successful as I'm currently world record holder in both the single (1:12) and average (1:14) records.
First of all the megaminx itself
Personally I use a nice looking mefferts 12 colour megaminx. They are currently out of stock at mefferts.com though you can preorder one at the moment. After you get one of these you should first modify it a bit for speedsolving. Take off the centrecaps and change the springs with slightly shorter and less stronger ones. And of course lubricate.
I would NOT recommend one of these, although they are very cheap I have a hard time to get even sub-2 minutes. They turn bad, the recognition is horrible and well, just don't get one of these unless you are not interested in speed which I can't imagine ;).
Seconds of all my notation: I use the normal moves as on a 3x3 cube only with some extra stuff. On the megaminx a U2 is different from a U2' (which is the result after a U3 move). Also if I say BR or BR' I mean the back face attached to the top face but since there are 2 of them I mean the RIGHT one (BR = one move).
Third of all, the method in steps.
I assume you have a mefferts megaminx so I show the pictures with that colourscheme but of course you should be able to get it with any other minx too.
The star The same as on most 3x3 methods, solve the 5 edges that belong on the white face.
The first 5 pairs Like on the CFOP method on 3x3 fill up the 5 slots you just created.
The rest besides the last layer Finish up the rest of the puzzle besides the last layer. 
Solve the last layer
Begin with step 1: Star and pairs