I did this on Windows 8 32-bit and I had NO problems with it what so ever. Just works.
First you need to install Java JDK if you haven’t one installed already. Choose the one that fits your computer and setup.
Next you go to Android SDK page where you click on “Download for Other platforms” and scroll down so you see SDK Tools Only. If you want the entire ADT bundle, do download that. But, this is only to get the SDK tools like ADB and ADM and such.
Download the version that fits your computer, Windows installer for me, and what this guide is based on.
Run the installer for it, it WILL check for installed JDK so make sure it’s installed first. I selected my own path for it since I want to get to it easy. When it’s finished, make sure that you are “start sdk manager” ticked.
There you tick both the SDK tools. That’s about it. Will in later posts cover how you actually use the Android SDK tools.