How do I zip up ALL files in one directory and then unzip them into another directory?

man tar
man gzip

tar -zcf <filename.tar.gz> </path/to/dir/to/"zip">

Ex:
tar -zcf zipped.tar.gz /home

That creates a gzipped tar file archiving everything in /home.

To unarchive:

tar -zxf <filename.tar.gz>

As clockwork recommended, I'd read 'man tar' carefully.