D.O.N.T. stands for Disturb Opponent's NoTrump.

When the opponents have opened with a strong 1NT bid it is not very likely that the hand belongs to your side. Still, anytime you can put a wrench in their works you should strive to do so.

D.O.N.T. is based on the philosophy that you would like to interfere when you have a distributional hand, but would just as soon defend if you are balanced. So a fundamental principle is that you should only invoke D.O.N.T. when you have at least 2 short-suit points, a singleton or 2 doubletons. Another way of looking at that is that you will use D.O.N.T. only if you have a 6+ card suit or a 2-suiter of 5-4 or 5-5.

Here's how it works.

If you have a 6-card suit you double the 1NT opening.
Partner is required to bid 2♣. This is just a relay bid.
If your suit is ♣, you now pass. Remember, you're only hoping for a partscore.
Otherwise you now bid your suit and partner passes. Again, you're hoping to play in a partscore.

If you have a 2-suiter, you bid the LOWER suit, even if it is a 4-card suit.
If partner can stand that suit she passes.
If she is better in ALL suits higher than that one she bids the next suit up the line, which you either accept or bid your other suit.
The only time partner can break this pattern is when she has a 6-card suit of her own and hates what she figures to be your two suits.

There is no built-in point requirement for using D.O.N.T., but common sense should prevail.
If the 1NT opening has been followed by two passes you are in the balancing seat and you can initiate D.O.N.T. with a pretty weak hand - as long as you meet the distribution requirements. You should be safe to do this because Opener's partner has advertised fewer than 9 points with his pass.

On the other hand, if your Right Hand Opponent is the 1NT opener then you are what is called the 'Immediate' seat. In this position you should have some strength, perhaps 12 points or more. This is necessary because the next player is still an unknown quantity, and may be just laying in wait to slap a penalty double on any foolish action you take.

Lesson available.