That doesn't make much sense.
When you download the free Stuffit Expander from Allume.com, it should come as a .dmg (disk image). This should automatically open with Disk Utility (well, BOMArchiver specifically) and mount on your Desktop. In the mounted disk image, there should be an icon to install Stuffit Expander. You should simply be able to double click it and it will go through the installation rigamarole.
If you're new to Macs, are you using Internet Explorer? Try using Safari instead.