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Well, uh. Form is always a problem if you don't have tonality since form has always depended on keys and modulations. Once that's gone, you just have to start making up your own "form" since tradition doesn't account for atonality.
With the obvious out of the way, I'd suggest you look into working maybe with 12 tone technique as well as intuitive/free atonality. Remember that length isn't really so important (Webern was a fan of brevity, after all) it's more important that you get down what you want to hear than if it's "stable" or "cohesive", since those two adjectives mean nothing unless we define what stability means or cohesiveness.
In essence, you have to know if you want to work with avoiding tonal elements, such as having chord built on 3rds, otherwise consonant intervals one after another which hint towards tonality. ETC. To really get into the atonal "sound" you have to consider dissonances, specially things like minor 2nds and major 7ths, tritones, etc, as valid intervals that don't need to "resolve" anywhere. In other words, there's no such a thing as dissonance and consonance in atonality, since both concepts are based on specific handling of such intervals. When all is treated the same, any difference beyond the actual quality of the sound ceases to exist.
That's also one crucial element which distances the "sound" from something tonal. The thing is though, that Berg incorporates tonal elements even in his atonal pieces, but the way he does it is different. There is a sense of harmony but it's very precisely twisted in the details so that it's never clear if it's there at all. By Schoenberg you get tons of traditional elements, but again, used in very different ways and contexts. Webern was, from the three, the one that worked purely with intervals the most. Though obviously, the phase of free-atonality is mostly interval work, by Webern it's intensified.
So yea.
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