Coyote

Playing as Coyote, your movement direction is aligned with your camera direction. Pressing a different direction will cause the character to walk in a very tight circle until facing that direction relative to the camera.

You nearly always want to be sprinting as Coyote, as walking is extremely slow in comparison. Jumping doesn't appear to affect your speed. Other than sprinting, there is not much you can do to go faster as Coyote.

Sometimes when you are jumping onto a rock or geometry at a higher level, you will want to be just slightly away from the wall, because jumping against the wall tends to get caught and eat your jump.

Crow

Crow is how you will get most of your speed. As Crow, your directional movement is no longer tied to your camera direction. Pressing left or right will change your flight direction independently from your camera direction. Tilting forward will cause you fly downward and increase your speed, while tilting upward will cause you to fly upward and decrease your speed. If your speed gets very low, you will slowly descent with very little horizontal movement.

Even without much height, just switching to Crow and using that little bit of height to descent as close to the ground as possible can get you more speed than sprinting as Coyote. You get a small speed boost right when you shift to Crow, which can be used to gain a little bit of height even without the boosts.

Multiple

Combining multiple shift forms is how you can get the most out of your speed. The crow dash movements will only take you so far. To help maximize your horizontal movement, you can use Coyote dashing. This is where you shift to Crow, and immediately as your dash becomes available, use your forward dash and shift back to Coyote as soon as possible. With this method, the impulse you got from the crow dash will be transferred to Coyote, who has a bit less of a speed falloff than Crow, and this will send you forward a good amount. As soon as you touch the ground, you can jump and repeat. If you have unlocked the coyote long jump, you can use that when you land to help maintain just a bit more of your forward momentum.

This technique can also be applied using the crow boost up, to get some quick height. The disadvantage is once you boost up, you have limited movement and are stuck as Coyote until you land.