When you have at least the top end of the opponents' 1NT range, or you have a long solid suit to lead, what do you do when they open 1NT?
YOU DOUBLE.
When you double 1NT, what do you want? You want them to pass meekly with a weak hand and get a large minus score.
Obviously, if your partner has a very weak hand he will take the double out if he thinks 1NT doubled may make.
Now, if your partner opens 1NT, it is doubled, and you think partner will go off (for hundreds) - you need a rescue system which may not cost you the hundreds that leaving 1NT doubled in undoubtedly will. This system is called Wriggle or sometimes Rigal.
When your partner's opening 1NT is doubled -
1. You have a weak hand but with a 5-card suit - simply transfer to it i.e. redouble tells opener to bid Clubs, 2 Clubs transfers to 2 Diamonds etc.
2. You have at least 9 points and happy at the prospect - PASS. This should be alerted as it is a forcing bid. Opener is required to Redouble if the next bidder passes. You can then pass the redouble if it is passed back to you - how exciting. They may well take it out, however, into their own contract.
3. You have a weak hand with no 5-card suit - make the Pass bid as in 2. but when the redouble is passed round to you, now bid your lowest 4-card suit. Partner now knows you are weak and can pass your bid with at least 3 cards, or can take a chance with his/her lowest 4-card suit which you can now pass or even bid a second 4-card suit. During this time, however, the opponents will often come in and bid their own suits and let you off the hook.
When you open 1NT with a 5-card suit and it is doubled, and partner passes, you can of course now bid your 5 card suit naturally instead of redoubling.
There is a variation that some partnerships play - this is that the opener's partner bids 2C as Stayman. This means that the transfer to 2D via 2C is not available and so, with a diamond suit, responder initially redoubles (an apparent transfer to Clubs), and then bids 2D after opener has bid 2C as requested.
This system is not difficult, and is worth learning as many people play it. Anything has got to be better than passing partner's 1NT doubled if you have nothing, with the inevitable minus 500, 800, 1100 etc.