Most Android devices support unpacking of ZIP files via the file manager, and do not normally need any additional software.
If your Android device does not support unpacking, try using the files app from Google, which is 100% free.
In most cases the process will look similar to this, but the process may vary slightly between Android devices.
Step 1: Locate the file you want to unpack
Step 2: Select the file by clicking on it
Step 3: Choose 'extract'
Step 4: All done!