The Android app is insanely picky, particularly if you're on ICS it seems.
First step: Force Close the process via settings. After it gets stuck in the loop of insta-crashing with just that black screen, the buggy process is usually still running in the background and you have zero chance of a successful launch until you kill it and start afresh. This should allow the app to relaunch properly, and you should get at least as far as the main app screen before it crashes next time. (You'll need to repeat this step, at the very least, each time you get into that black-screen crash loop -- it's actually best to do it any time the app crashes, period.)
Second step: Reboot the phone. Pain in the butt but usually works to clear the process completely and at least give you another completely "clean" launch attempt.
Third step: Clear local Spotify data via Settings. This will delete your login credentials and offline playlists (even more of a pain in the butt, I know) but should give you a shot at a fresh launch and login attempt. The crashes I've seen have generally been associated with the app going online and syncing up with your account, so you it should run fine up to that point at least.
Fourth step: Uninstall/reinstall. Yeah, nobody wants to hear that solution, but it sometimes works. Temporarily at least.
Fifth step: As I mentioned, the Android crashes seem to be related to the app syncing up with your account, particularly when retrieving and updating playlist names and counts. From anecdotal evidence on the forums (and personal experience), it seems the crashes are often related to either high numbers of playlists, or particular playlists that somehow get bugged and freak the app out. There's no way of knowing which playlist that is, but I've found that deleting a few "excess" playlists (often stuff I randomly subscribed to out of vague interest) via the desktop app has cured the Android app on next launch. Anecdotal, unproven, and impossible to know exactly which playlist is the issue. But may be worth a shot if you have some playlists you can trim off your account.
Couple of other things worth noting...
- Most crashes do seem to be related to the app syncing with your account. (Not syncing as in offline syncing, just making sure it has your latest list of playlists, etc.). You'll see the app launch, get to the main playlist screen, possibly even see it trying to update playlist names and data, then it'll freeze and/or crash. Since it's being online that seems to trigger the crash, some people (including me) have had success either switching to airplane mode to disable connectivity before launching the app, and/or switching to the Settings tab in the app and enabling offline mode asap. Of course you're stuck with offline playlists only then, but hey... it's a start!
- My suggestion: If you're able to get as far as the main playlist screen when you launch, TOUCH NOTHING! Seriously. I've found that my immediate reaction on opening the app is to scroll up and down the playlist screen, at which point it becomes unresponsive and crashes. I've found the app is a lot less inclined to crash if you keep your fingers off the screen for 10-20 seconds while it logs in and syncs playlist info with your account. It's not foolproof but it does seem to give me better odds of avoiding a crash.
No definite solutions, sorry. But hopefully you can get a workable scenario with a combination of those tips. After 4-5 months of unending crashes, stuck-in-offline, and other stability issues with the Android app that made it unusable, I seem to have found a strategy that works for my device and account, and it's been running semi-reliably for well over a month. Good luck. 🙂