For all who have no idea how to just save let alone upload that abomination, there are a few scripts helping with the procedure. It's still tedious work though, so you may want to wait until uploading these things is integrated into danbooru.
You still want to go at it?
Toks wrote a ruby script that does bacically everything you need, this is going to be integrated into danbooru in the near future. You can find it here.
Problem is, it's quite complicated to install, especially the imagemagick part, especially on windows boxes. You can find info about that here and here.
There is also a perl script doing most of the work, but it's buggy. You can find it here.
There is also a tool that downloads the zip with all the pictures, you have to do most of the evil work (converting) yourself, though. You can find it here.
Here is a bookmarklet doing the same as above tool:
javascript:window.location = pixiv.context.ugokuIllustFullscreenData.src;
If you want to convert ugoira, be warned: The framerate is variable. Most image tools do not allow that.
Here is a bookmarklet to get the frame delay data:
javascript:var%20str%20=%20"";var%20frames%20=%20pixiv.context.ugokuIllustFullscreenData.frames;for%20(var%20i%20=%200;%20i%20<%20frames.length;%20i++)%20{str%20+=%20frames[i].file%20+%20":%20"%20+%20frames[i].delay%20+%20"\n";}alert(str);%20window.location%20=%20pixiv.context.ugokuIllustFullscreenData.src;
Here is another tool for windows boxes, that downloads ugoira and converts them to gif, the timing is wonky, though. You need at least .net 4. You can find it here.
More converter scripts for webm and GIF, same requirements as Tok's script, find them here.
There's a new script for GIF converting, find it here.
That should be all for now.
Edit: Added yet another tool.
Updated