Astro file manager. It's in the market. It's free. Once in there, press menu>new>Zip File, enter the desiered name (be sure to add .zip at the end)
Then, to put files into it, long-press on the desired files (or click "Multi" at the top to select more than one, then long-press), select edit, move, then navigate yourself into the newly created .zip folder, press Edit at the top, then select paste.
And you're done.
Enjoy! (Astro will also allow you to OPEN/extract .zips)
I got your back! I actually had to think about it. I saw Astro suggested here MONTHS ago, and use it so damn much that I forgot it's not stock/common knowledge!
:icon_ banana::icon_ banana: