Easy. Do you have Winzip? If not, download it here: www.winzip.com
Winzip is NOT required because you can use any program that can open and extract from .zip files.

Anyway, after you've downloaded the .zip file, open it up and extract all the tilesets (these end with .j2t) and levels (these end with .j2l). There may also be music included, in which case you will probably want to excract those too. If there are no tilesets or music files, then it is likely that the author uses official tilesets and music. Hm..extract where? Right into your main JJ2 folder (for example: C:\Games\Jazz2\).

Then you can run Jazz 2, select singleplayer, select the Homecooked levels 'episode', and find the level you just downloaded. (Remember that if you have too many homecooked levels, JJ2 will not show them all...only the oldest ones).