From Quake Wiki
Trick Jumps are maneuvers that allow you to achieve a speed, height, or distance beyond what is usually possible with the physics of Quake. In general these 'features' were not intended by the designers at id Software, though there is some evidence that at least some of them were known to the designers during development.
A ramp jump is one of the easiest trick jumps to accomplish. Simply run up a ramp and jump just before reaching the top. The upward velocity of your jump is actually added to whatever upward velocity you had while running up the ramp, resulting in extra height.
A strafe jump can be used for two purposes -- first, to extend the distance of a jump, and second, to jump to an area that could not be reached without bending the jump around some obstacle. The jump is accomplished by running and jumping at an angle to your actual goal, then using a strafe key and the forward key at the same time, while turning your view to steer the course of the jump. A good use of this is to jump across the lava from the Rocket Launcher room to the Super Shotgun room in DM2.
Simply have a Rocket Launcher, armor is favored, aim down, jump, then fire a rocket under to propel yourself a bit more.
A grenade jump uses the same principle as a rocket jump, except that you have to stand/run over the grenade and jump just as it explodes. The timing required to do this correctly will take some practice. If the floor below you is flat and you are in no rush, an easy timing trick is to shoot the grenade straight upwards. The grenade will fall down exactly at your position and bounce. It will explode when it hits the ground the second time.
Grenade + Rocket Jump
Ensure that you have the grenade launcher, rocket launcher, at least 2 rockets and adequate armor and health before starting, the more of each the better. Select the grenade launcher and fire a grenade aiming to land on a particular spot (the launch position), one way to do this is to fire vertically in to the air once you have found a nice spot to perform your jump. As soon as you have fired the grenade, switch to the Rocket Launcher and at the point that the grenade lands for its second bounce move to the launch position and fire a rocket directly at the ground. If you time it right, so that the rocket hits the ground at the same point that grenade explodes, you should find that you are able to jump significantly higher and longer than with just a Rocket Jump or Grenade Jump. The disadvantage is that it requires more ammo/weapons, usually takes longer to perform, which can be problematic during battles, and does more damage to your player. If you do this with low health, you will usually end up in an embarrassing crumple on the floor with your opponents standing around openly giggling at your failure.
Voreballs and Ogre grenades are obvious alternatives to using your own explosives to get a boost. However, any enemy attack that damages you will also give you a physical push away from the source of the damage. The relative position of the monster determines whether this push is upwards, outwards, or downwards.