Proceed chronologically, and gradually. Start with the latest/most advanced period or school that you can currently comprehend, and increase to the next one above. After you've "mastered" the next one, iterate. (Of course, there isn't exactly a total ordering, but it's close enough for this to work.)

For example, if you can "handle" late Mahler, you should be able to handle early Schoenberg (which actually came before late Mahler, as it happens). In which case you should try your hand at middle Schoenberg.

After you've mastered late Schoenberg (and Webern and Berg, etc), you're ready for postwar music. When you get to the point where the most advanced pieces of the 1950s and 60s, say, are comprehensible to the point where you can sing them to yourself from memory without having heard them in a while, then you will probably find the advanced music of our own time to be reasonably accessible.