From QuakeWorld Wiki
This page contains a step-by-step method describing the mechanics of "bunny hopping" in an effort to teach someone who does not know how to do it. Most of the techniques described here were invented before 1998, and no later than 2003!
There is also a video tutorial explaining these steps.
The bunny hop is jumping, strafing, and turning that, when combined properly, allows the player to accelerate beyond the 320 pps cap imposed on just holding "forward".
 Simple movement
 Zig Zag
This is the first element of acceleration you will learn on top of the 320 forward speed. To continue, you will need mouselook enabled (as you always should). Make sure your viewpoint moves around when you move your mouse around.
To execute zig zagging, first press your forward movement button. You are cruising along at the usual 320 pps. Now smoothly and slowly move your mouse left and right, and watch your speed counter. It should be going over 320! Congratulations, you just did a zig zag.
 Advanced zigzaggingQDQ team (before there was even a "QDQ team") and that makes sense because zig zagging is the same as bunny hopping only without jumping.
The advanced (or complete) zigzag also includes strafing in the same direction as you are turning. As you are moving your mouse left and right, press your strafe key in the same direction. You will see that your speed is increasing even more.
Zig zagging is the base skill of bunny hopping and the better you are at zig zagging, the faster your acceleration will be, and the bigger gaps you will be able to clear with your initial bunny hop, which is also an important skill in bunny hopping.
To do an efficient zig zag, you should study how your speed counter changes when you move your mouse as you are walking forward. Notice how less effective the speed increase is when you shake your mouse left and right too fast. Likewise, it is less effective if the mouse is moved too slowly. The trick is in strafing in the same direction as turning, changing strafes in sync with changing turns, and turning (or "curling") the mouse at just the right speed. Also note that the critical speed of rotation that yields the most acceleration is, subtly, inversely proportional to your speed, in other words, the faster you move the slower the critical rate of rotation.
 The final step
Once you are comfortable with the strafe-and-turn zigzagging, all you need to add is jumps. The only trick here is to jump at the same point as you change the direction of your strafe-and-turn, *and*, once you start jumping, to let go of the forward button. To continue your first bunny hop into a sequence of bunny hops, let go of the jump key in midair, and then press it and hold it again. When you land, you will jump again immediately. Then, repeat the release-and-hold-jump technique in midair.
 Another method
Once you know the above method of zig zagging and bunny hopping, you can also divide your bunny hop skills in a different way, to practice them.
 Standing start
Alternate this for a while to get the hang of it. You will still be more or less in the same spot not going anywhere.
Now, start the hold-jump-release-and-hold-jump technique discussed in "the final step" above. That is, press and hold jump, and before you land, release the jump key and then hold it down again, so that there is a continuous sequence of jumping. If you do this correctly, you will see that you are accelerating forward, without ever having pressed the forward key! This is the very essense of bunny hopping that you should practice.
 Advanced bunny hopping
 Sideways bunny hopping
Take your usual bunny hopping, but instead of let going of the forward key on the first jump, keep it pressed, and instead add an extra angle (about 45 degrees) on top of your turn. The effect is that you are never looking directly forward, but are still accelerating, and is this useful for setting up a shot on the fly while turning around a corner (for example GL->RA on DM6).
 Circle strafing
Same as sideways bunny but this time there is no turning at all, and if you turn, the extra angle on top of the turn has to be about twice as much (around 90 degrees). The effect is that you are looking in the same direction as the object around which you are jumping. This is useful to confuse opponents in circular fights, such as on the upper GL on DM6, or on Amphi, etc.
 Backwards bunny hopping
This is fun. How to do it is an exercise left to the reader. (Do the same thing as regular bunny hopping, only everything is reversed...)
 Backwards sideways bunny hopping
This is fun also. A notable example is one variation of the backwards curl-jump to MH/RA on DM2.
 Backwards circle strafing
I'm proud of independently "inventing" this one... :D
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