As an intro, you can watch Zoot here or try some of the excercises I outline below. FYI: "turbo" used to be called PQL which was based on challenge pro mode or CPM, so you'll see the terms used interchangeably sometimes.
http://www.youtube.com/watch?v=HuzfxcSfZOE

AIR CONTROL

First load a map where you have some space, theatre of pain or black cathedral are good choices.

step 1: find an open space. hold jump to bunnyhop.

step 2: press W and move forward in a straight line while hopping like a killer bunny. if you know how to strafe jump you can gain speed like this.

step 3: when you are bored of hopping in a straight line, start moving your mouse left and right. keep W pressed. notice how you can turn corners in the air as long as the turn isn't too sharp.

step 4: practice moving around the map like this, just holding jump and W and turning while you are in the air.

step 5: now you can try to gain speed around corners. to do this, instead of holding W, only hold the strafe key on the side that you are turning into: Hold D and move the mouse right, hold A and move the mouse left. notice you gain more speed this way.

step 6: experiment to see how fast you can go. on a map like dead and gone you can practice going in a circle around the middle of the map holding only jump and 1 strafe key and gain speed as you turn.

this should get you started. to learn more you can watch some of these videos too. Some are for CPM or the game Warsow which have similar physics.
http://www.youtube.com/watch?v=Oj_M4M61aTA
http://www.youtube.com/watch?v=sKQcbdLoy1s
http://www.youtube.com/watch?v=RrFCPRcDKAk
http://www.youtube.com/watch?v=1Y6t07VID4w
http://www.youtube.com/watch?v=xf-8J8pSGr4
https://www.youtube.com/watch?v=uTx_rpSX2rs

RAMP JUMPING

ramp jumping and step or doublejumping are key aspects of Turbo and CPM physics. Holding jump when you run into some stairs is the easiest way to see the effect. Unlike CPM, stairs are basically treated as ramps in QL Turbo, all ramps transfer your horizontal momentum into vertical momentum, which can boost you up to great heights from stairs or ramped surfaces. Step or double jumping is similar and gives a boost with extra jumps in short succession, accomplished by jumping as you hit ledges on your way upwards; the second jump off the ledge will boost you much higher than the first jump (you can even boost off of player's heads!) To see the full potential, load up the map Use and Abuse.

Step 1: notice the stairway opposite the high passage to mega health, perfect for launching with a left turn in the air to quickly grab the mega

Step 2: from the railgun with a view of the stairs, get a solid star with a few strafe jumps and when you hit the stairs tap or hold jump, and as it begins to launch you higher, hold left strafe only while turning left towards the passage to mega/teleporter.

Another great jump is on Aerowalk from the bottom of the red armor stairs straight up to grab RA. From the lower tele you can time a jump to land just before the first step and tap or hold jump to boost up to the armor ledge.