I would presume it's either a SIT or dmg file right? If so, then double-clicking will probably uncompress/mount the file. Then it depends. There might be an installer inside or just a program you can drag & drop to your applications folder. If it's an installer then yes double-click it.

If you have trouble opening the sit or dmg, then drag & drop it. eg: D & D a sit file onto stuffit expander or a dmg file onto disk copy.