In this guide I will list out your movement options in the game:

Before you have both the Cloning device and the Swapping upgrade and when swapping or creating clones is not possible, the fastest way of traveling is by bunny hopping. This is done by pressing the jump button as soon as you land to negate/reduce the slowdown that you get from the walking animation. You make the most distance by using longer hops instead of shorter hops, so hold down the jump button during each jump. Bunny hopping is most effective if you land on a downward slope, which will result in a big speed boost.

When both swapping and cloning is possible, the fastest way of traveling is by quickly creating a clone and then swapping to that clone. I call this movement technique 'blinking' (because it's similar to the blink ability in games like StarCraft 2 and Dishonored). Since the hitbox of the clone sprite is smaller from the top and the bottom than from the sides, this means that quickly blinking up or down is more difficult than left or right. However when blinking left or right, make sure to correct for gravity pulling the clone downwards.

Sometimes it may be benicifial to bunny hop instead of blinking if you are one hop away from a ledge. One blink is a little faster or about as fast as a bunny hop, but by bunny hopping you already have some downward momentum as you move past the ledge (as opposed to blinking, which sets your vertical speed to 0), which also accelerates over time. This means you'll fall down a bit faster.