Hi, I've been DJ'ing snce 1998, focussing mostly on the trancey style of music.
As for the DJ'ing side, it all firstly depends on what type of DJ'ing you want to learn.
The options mainly available now would be mixing CDs (using something like a Pioneer CDJ) or mixing MP3s using a laptop and DJ controller. You can get the latter considerably cheaper than the CDJ option, but again the choice is yours.
I began on vinyl, then later progressing to MP3. As for the basic artform, the first thing you will be learning is beatmatching, being able to sync to tunes up to the same tempo and hold them there. Granted, much hardware now has facilities that can do this for you, but many DJs feel this takes away from the actually artform of DJ'ing and is a bit of a cheater's game.
So firstly make sure your beatmatching skills are solid. Aside from this, you will also need to know the structure of EDM music. If you listen to any professional DJ, you will notice that not only are tracks synced up tightly, but their musical phrases (events) are also matched. This is one if not the MAIN thing that sets apart an amateur DJ from a pro. So learn about the structure of music.
The final part technically is the actual mixing itself, using EQ properly. Judicious EQ use combined good EQ and phrase matching are what makes mixes sound great. EQ can be explained, but after a time it's more of an instinctive thing I think. When I'm doing a mix, I focus mostly on the basses of the tracks to avoid clashing, but the mids and hi's I adjust very quickly an instinctively based on a combination of feeling and hearing, this comes with experience.
Aside from all this it's all about finding tracks that complement each other. You need to be always thinking ahead of what you are playing, what will mix in well and what will sound good, also what direction you want to go - an upward curve (more energy an excitement), a downward curve (a kind of mellowing out) or a flat line (steady ongoing rhythm). Most importantly though, is to do your own thing and have you own kind of sonic stamp.