Triac connection for my project
You can't do this with 1 monostable multivibrator (MMV), you'll need two of them, like also Federico Russo says. A timing diagram will make this clear:  



MMV1 gets triggered on the mains' zero-crossings. (You'll need a detector for that. See for instance this question). with a potmeter you can vary the period of MMV1. When MMV1 times out it triggers MMV2, which in turn triggers the triac's gate.

Now triacs, once triggered, remain on as long as there's current through them. For a resistive load, where the current is in phase with the voltage, that will be at the next zero-crossing. Then a new cycle starts with the triggering of MMV1, and some time later the triggering of MMV2 and the triac.

The pulses from MMV2 must be short. If they are several ms long they may extend longer than the next zero-crossing, and retrigger the triac. The triac will then be on all the time. The rule is: t1 + t2 (delays from MMV1 and MMV2) &lt; half a mains period. 

Frederico already pointed out that everthing connected to the triac is connected to your 230 V (or whatever your mains voltage is). Touching the circuit can be lethal. If you use a potmeter for the dimming, use one with a plastic shaft. The best thing, though, is to use an opto-isolated triac. You'll find post for that here on EE.SE. Just make sure that the opto-triac is not a zero-crossing detecting type.