First and foremost, maths and statistics. But the interesting question is what to apply them on.
I believe it's best to first apply them to myself: figure out how good my own predictions are, and make sure I'm ready to face my own mistakes. No point in getting cornered for maximum short-term profit. For the actual predictions, I use a combination of simplified models, psychological ideas, and historic comparisons, all fed by whatever indicators I can get a hold of: news, forum stats, various forms of trading volume, ...
The difficult part for me is calibrating a model after I have some rough idea. What's the scale, growth, sentiment of Bitcoin? And I have to cope with horribly foggy indicators. I'm not really versed in history, so I have to look for past events that hold similarities. This can be within Bitcoin for short-term things, or old stuff like the DJIA around 1930 to understand what happened in the big 2011 Bitcoin bubble.
Don't take this too seriously, I'm still a noob. I'm not even done "calibrating" myself, don't know how many mistakes I do on average. So this post could be one. 
