Fox-trotting

Fox-trotting is a simple movement technique that can increase many character's dashing speed. It uses the speed of most character's initial startup dash, which is more often than not faster than their speed at full sprint, to create a faster continuous run speed. Characters most notably affected are Fox, Captain Falcon, Roy, and Marth.

To perform a Fox-trot, dash forward, return the analog stick to neutral, and dash forward again. Repeat as desired. The timing is different for every character but fairly easy to pick up on. Fox-trotting can also be performed by jump-canceling your dash into a wavedash and then restarting the run animation, and by dash-canceling your run into another dash.

In Brawl, there is a small chance that one will trip when they dash, thus attempting to Fox-Trot will increase your odds of tripping and leaving yourself open, but will reward the user if not.

Dash Sliding, a variant of Fox-trotting, is described as a constant state of dashing. It is done by mashing the control stick in an direction, and then returning it to neutral, then repeating, similar to a Foxtrot. But when doing a Foxtrot, you had to dash-dance to change directions. In a Dash Slide, you can shield cancel out of it, for a fake out. Also, since most characters hunch over in the animation, you are a smaller target for an added bonus. Can be used as a mindgame, or as a speed advantage over your opponent.

The term was coined by Clan, Hoboking, and Legend of Brawlcentral. You can see the whole thread: [1]