Any% is the fastest way to finish the game. Finishing refers to shooting out of the final wire in the Moon Kingdom during the Bowser escape sequence.
The route in Any% is mostly modular, meaning each kingdom has it's own route that doesn't impact any major aspect of the route in another kingdom (with the minor exception of the coin routing)
The complete route document can be found here.
Smallant1 made a great series of tutorials oriented towards beginners. This is a definite must watch for anyone looking into running the game.
Progression Video Edit
Smallant1 also made a video explaining how the any% category reached the point where it was beaten in under an hour, which can be found here