diabolo (thing)

Tips:
-- Make sure the string isn't too long. If you can't pull the sticks apart and get the string taut, it's too long. If you hold the sticks together and in front of you at about waist height, the bottom of the string shouldn't touch the ground.
-- The diabolo's stability is directly related to the speed at which it is spinning. If your diabolo veers too much in any one direction, you might want to try increasing the speed at which it spins.
-- Rolling the diabolo on the ground (from left to right (diabolos can be and are used in the other direction, simply reverse all instructions)) is a good way to build up speed. Start rolling the diabolo slowly and build speed up. This helps to keep the diabolo from banging about too much as you roll it across the ground. Then lift the diabolo into the air with your right stick and try to keep up the speed.
-- To maintain speed and stability, I like to think of the jerking action as more of a pulling motion. Hold the left stick as still as possible (it will bounce a bit, and that's okay, but don't consciously move it about) while you make fast, but not too jerky upwards pulling motions with the right stick. As it spins faster, you can increase the length of your pulling motion.
-- The diabolo will try to tip forward or backwards. Fixing this is slightly counter-intuitive. Continue the pulling with your right hand, but if it the diabolo tips forward, move your right hand towards your body a bit and do your pulling there until it straightens out. If the diabolo tips backwards, move your right hand forward away from your body and pull out there. Don't direct your jerking towards or away from you. Continue to pull upwards, just change the positioning of your hands.
-- The diabolo may rotate around a vertical axis and be stuck a little off-angle. The simplest way to fix it is simply to turn your entire body around until the axis of rotation of the diabolo is perpendicular to your shoulders again. There are other ways of fixing it, but this is the easiest (especially if you don't have an audience).
-- Intermediate diabolo spinners may use an altered, whipping technique to gain much faster speeds and accelerate to those speeds at a higher rate. It's actually a little trickier than it looks and beginners will frequently find themselves able to do tosses and other tricks before they master this seemingly simple gimmick. It involves whipping the diabolo from right to left with a motion that incorporates both hands. It often involves repeatedly crossing and uncrossing the hands. It's tough to teach someone in person and, in my experience, is something that is learned through frequent practice and fumbling until it suddenly clicks. If someone with better instructional skills than me can give a better description, I'd welcome it.
-- Occasionally the diabolo will bump into something and start to wobble crazily. This isn't as bad as it seems at times. Simply revert back to the simplest gimmick of holding your left hand still and pulling with the other. The diabolo will recover after a bit (usually) and you can get on with the fun.
-- If you miss a catch, it is also not necessarily over. Most modern diabolos are made mostly out of rubbery plastic and will bounce quite high. There's usually a second chance to catch it on the bounce. If you play it right, you can make it look like a trick rather than a save.

Tricks:
Toss -- This is a very easy trick and still a crowd pleaser. When your diabolo is spinning, pull the string taut by pulling the sticks apart very quickly. The diabolo will shoot skyward, much further than you could have thrown it by hand. To catch it, hold your arms up and keep the string taut. Just make sure that the diabolo lands on the string. Due to the shape of modern diabolos (like an hourglass (or an egg timer (depending on which side of the Atlantic you're from)) on its side), you don't need to hit dead center. The diabolo will definitely start to pull the string down unless you're holding it really tight, which is not good. Let the string drop down to a normal position and continue as before. For a nifty trick, instead of letting the string dip down all the way, pull it taut again immediately. The diabolo will pop back up a bit and come back down. You can keep this up indefinitely, and it looks good when done over your head. The diabolo can be tossed several stories into the air without a whole lot of effort or skill, and unless it gets tossed off in some other direction, it's pretty easy to catch. Sometimes you have to run after it if you give it a bad toss. You can make a show out of that too by sliding into place on your knees before catching it.
Cat's Cradle, Eiffel Tower, Spaghetti, etc. -- Each of these tricks operates on the same principle. Throw the diabolo really high to give yourself some time. Tangle up the string in some creative manner. Catch the diabolo on the tangled strings. It is preferable to choose a tangling that allows you to pull out of the tangle without leaving knots in the string. Some variations do not require tossing the diabolo. Some tangle up one of the sticks so solidly that you can let go of one of the sticks briefly.
Grind -- Toss the diabolo up a few feet and have it land on one of the sticks. It will make a grinding sound for a moment and you can toss it back up and catch it on the string again. Make sure the stick is perpendicular to the axis of rotation of diabolo and well-centered. Angle the stick up to the left slightly or the diabolo will roll right off the stick. If you can find the proper angle for the speed and friction of the diabolo, you can hold it for a few seconds longer. It loses speed fast, however, so don't hang on too long. You can pull a double grind by bouncing from a grind on one stick to the other.
Climb -- Get the diabolo spinning really fast. Then simply loop the string around the diabolo once so that the diabolo is not sitting on top of the string, but the string is wrapped around the center. When you pull the string taut, the diabolo will climb the string to the left, so make sure that your left hand is higher than your right. If it's spinning fast enough, you can make it climb a vertical string. This is another trick that causes the diabolo to lose speed fast, so don't hang on too long.
Suicide -- A suicide is a general name for any trick where you let go of one of the sticks. A simple suicide would involve swinging the whole assemblage counterclockwise (or anticlockwise (or widdershins)) around the right stick and letting go of the left stick. This doesn't sound like it will work, but it does without much difficulty. The hard part is catching the left stick as it comes back around. There are other varieties of suicides that involve winding the string around the sticks in a particular pattern. Some of these are actually easier to pull off than the simple suicide. Another variant can be pulled off in the same way as the simple suicide I described, but by letting go of both sticks. Again, things will rotate smoothly, but catching the two sticks is quite difficult. Sometimes this is called a duicide.
The Whip -- This is a great show-ending catch that is a bit easier than it looks. It's not easy, but it really looks spectacular. Toss the diabolo into the air, then put both sticks in your right hand, with the tips slightly apart. Step to the side of the diabolo so that your shoulders are parallel to the axis of rotation and swing the string over-handed as the diabolo comes back down. The trick is to lay the left half of the string perpendicularly to the axis of rotation over the center of the diabolo and the right half just to the right of the diabolo. Continue to swing about and the diabolo will sit at the bottom of the string, spinning merrily by itself.
Loops -- Lift your right leg over the string. Roll the diabolo towards the left end of the string and toss it up and over to the left a bit. Catch it on the right end of the string. It will roll down towards the left again, making it easy to repeat as many times as you wish. You can loop over just about anything, but another common method is to loop over your arm. Hold your right arm forward and bend at the elbow, making a right angle, and holdin the right stick pointing towards you, tucking the string under your upper arm. When the diabolo loops around, it will pull the string down far enough (if you let it) so that it will clear the bottom of your upper arm as it passes by. This trick is much trickier than the leg loop. You can actually loop the diabolo under and over both arms at the same time. When spinners use more than one diabolo at a time, they usually keep them looping around each other continuously unless they're doing some other trick with them.