In order to go fast, you're gonna need to do more than your basic walking.

Strafe Running & Slide Dashing

Holding either W+A or W+D and looking off at a 30-45 degree angle in the appropriate direction (Left for A and right for D) will give you a pretty decent speed increase. We've dubbed this Strafe Running.

Alternatively you can spam shift and gain a fair bit of speed by sliding over and over. We've dubbed this Slide Dashing.

I think it's faster to Strafe Run, but you can shoot enemies a bit easier if you're Slide Dashing.

Serious mode sliding

Serious mode uncaps the backwards movement speed, and a slide goes in the direction you're aiming. This means that if you start a slide while strafing backwards, serious mode will propel you at almost twice the speed of strafing

Movement methods comparison video