Most gaming companies create a Game Design Document (GDD). Its purpose is to contain all aspects of the game before actual development starts. It's mostly text, but it can contain rough sketches (mine have been just boxes with labels representing objects) to help give visual for how the game should play out. A GDD usually includes other parts of development, such as art style, target audience and target platform.
When my friends and I started working on a game project the first thing we did was create an elaborate GDD, and we found it a very good way to organize our thoughts through the design phase. A GDD isn't just for giant studios, it can help Indie developers too, group or single.
There are many online tutorials and examples for writing a GDD, a quick search should give you many resources to reference.