Download the software which will usually put a .dmg file on your computer. Double click on it. It will usually open a new "drive" on your computer with other things to double click to run an installer. If it asks for an administrator password, enter it.
Depending on the software, double-click the installer on it or drag the application to the Applications item in the Finder's sidebar. If the program is designed for Windows, you'll need to use that, CrossOverMac, or similar products.