Just a quicky, for most platforms you can get a free pkzip-compatible archiver from InfoZip. Please don't confuse ZIP archives with .tar.gz (sometimes called .tgz) archives, ZIP disks (the Iomega removable storage widget) or ZIP postal codes. They are all quite different.
If you run Cygwin, you have a unix-like layer on top of Windows, so can follow the Unix-esque instructions below. (Although if you use Cygwin, you likely don't need this sort of advice.)
In modern versions of Finder, you can select some files and ctrl-click for a context menu and choose 'Create Archive of n items' (or 'Compress n items' in the latest version). This will create a file called Archive.zip in that folder which you can send in.
On MacOS X, you could open a terminal and follow the Unix-esque instructions instead.
Put everything in a directory ('pics', for example), stand in the terminal one level above the directory and run:
% zip -r pics.zip pics/
If the zip command isn't installed, try talking to your administrator. If that's you - then you ought to know where to get it.
.tgz) is not the same as a zip file - although we could support them too if there were enough demand.
Put everything in a directory, right-click it in the tracker choose Add-ons, then Zip-O-Matic. Alternatively, follow the Unix-esque advice above from the Terminal.