Strafe Jumping is a good way to build up speed in Quake Champions, since normal movement is usually slower. To perform a strafe jump you need to walk forward and start by jumping while pressing left & strafing the mouse to the left at the same time, (W+Space+A+strafe left), when you're close to reaching the ground from your jump, jump again (you can also just hold space to permanently jump, but it's said to be slightly slower than a perfectly timed jump) while pressing right & strafing the mouse to the right. (W+Space+D+strafe right). If done correctly, you should be gaining speed. (There is a speed-o-meter option in the ingame gameplay settings to see how fast you're going)

Since this is tricky to explain with text only, here is a video of Rocket Jump Ninja explaining it in-depth

This should help you get started to improve your basic movement speed.