Hi and welcome,
Opening a zipped file should be easy by double clicking on it, because as far as I am aware
Macs have had the ability to open ZIP files since around version10.3. They can also open the more popular Unix archives, like TAR and GZ.
To check whether or not your Macs zip function is working correctly, take any file, right click it (ctrl-click), and select the "compress <item>" option, then when and if it zips up into an archive, try uncompressing the archive. If it all works then the problem lies with the specific files you've downloaded, rather than OS X's abilities to handle zip files.
For third party software I use SmartZip Pro but you can download
Stuffit Expander free.