I downloaded the 32-bit version and simply ran <home>/android-sdk/tools/android. No additional installations are necessary outside of the sdk.
In my .bashrc file I added
export PATH=$PATH:/home/torsten/Computer/Android/android-sdk-linux/platform-tools
so that I have direct access to adb, fastboot, etc.
Many thanks. Did as you suggested, seems to have worked - or, at least, there were no error-messages

. Next step, according to the web-site quoted above, is to launch the ADT by clicking on
eclipse, which does indeed start the ADT; when I click on
Build Your First App, however, the ADT does something for about 30 seconds and then dies

. Looks like I'm doing something wrong there. Don't suppose you have any further tips, do you? Thanks, once again.
Edit: I've just noticed that, whenever I run eclipse (which then seems to fail) and then want to shut the machine down, I get a message "
AT SPI Registry not responding", which I then have to manually kill. Could this be relevant

?