Another way to do it (without starting over, and easier) is to download cheatengine. http://www.cheatengine.org/.
It's a hex editor. You can click "Enable speedhack", set the amount of times you want it increased (ie, 1.3x, 2x or 5x) and click apply and it will set the process you selected to that amount of speed.
You can find plenty of guides on it around the internet.
This will also speed up any animations of both your characters and other characters, while the movementspeed mod only modifies your own characters movement while everything else in the game stays the same speed.
Neither solution affects the combat, so no need to worry about that.
If you want to use the movementspeed mod without starting over, you can follow Rhidian's guide here on the forum of how to copy the .meta files around to make it work.