Your iPad does not come with any native - meaning pre-installed with your device - applications for managing or opening files. You must first download an app for this. Here is a free file manager app:
Once you have this File Manager app installed, let's walk though an example. You've encountered a ZIP file on the Internet and clicked to download it.
You may be presented with a dialog box asking you which app to use for opening the file. Click "Open in..."
Next you'll be presented with choices. In this case chose "Open in FileManager".
The file will be downloaded to FileManager.
Click on the file to UNZIP it. Click "Unzip" when prompted to confirm..
The files are unzipped.