Honestly, all it takes is to just learn what guitar parts you like in the songs. Once you learn enough, youll automatically understand how to produce the style.

For instance, Marty Friedman solos in old megadeth were quite unique, and I wanted to know what he was doing so I could incorporate that sound in my own way for my own material. So I simply learned the solos! I now understand his style, thats all there is to it.

For Rush, there should be plenty of tabs out there on the internet you can learn from. I would recommend a guitar pro/powertabs type tabulature program, thats where the good accurate tabs are.