To install, download the compiled .jar below and replace it in your Azureus directory.
The patch is just one line, that will put more priority on the first pieces, if you select Download pieces in order from Tools→Options→Transfer. With this disabled, downloading happens normally.
Be sure to rename the .jar file to Azureus2.jar after downloading.
If Azureus asks to upgrade to a new version, you should either check this page for a matching .jar (and send me a mail to compile one if I haven’t already), or not upgrade to the new version.
Here is how the download progresses using the patch: