Here is a list of places to download free zip software. I DO NOT ENDORSE ANY OF THEM. I'm only listing the links for you to make a decision on which zip software download you may want to try. I use WinZip, but it's not free.
List of 5 free zip software
WikiHow - FYI - I didn't read the whole article, but it looks like you can download zip files and open them without having zip software. The only downside is if you want to zip files.
After you download your zip file, right click on the file itself
Select "Open With"
Select "Windows Explorer"
Your files will open right up. I don't know when Windows added this feature, but I like it. Unfortunately, I must have the ability to zip files too.
Ok, well, I hope these help. NOTE: Before downloading any file, make sure you have updated anti-virus software.