Bidding can be hard enough at the best of times, but when people preempt against you, life may become almost impossible. In order to combat this, it is important to play a good defence to preempts, and fortunately, the best defence is also the simplest.
Over the years all manner of defences against preempts have been proposed, but virtually all top players in the world now agree on how to defend against preempts. Double is for take out, showing a shortage in the bid suit and support for the other three suits, no trump and suit bids are natural. (The cuebid and jump to four of a minor are not entirely standard but are nowadays the way that most people play.)
For example, if opponents open a weak 2:
X: Take out, eg Kxxx x AJx KQxxx (Over this, you should play Lebensohl, see Newsletter 12)
2: Natural, at least five card suit, 12+ points (ie HCPs), eg AKxxx xx Kxx Qxx
2NT: 16-19, eg Kxx KJx AKxx Kxx
3: Natural, at least six card suit, a reasonable seven playing tricks. eg KQJxxx x AKx Kxx
3NT: A better hand, hoping to make 3NT, e.g. Ax Kx xx AKQxxxx
4: A good hand, hoping to make ten tricks. KQJxxxx x AKx Ax
3: Asking for a heart stop, based on a good minor suit, e.g. Ax x Kxx AKQJxxx
4/: Roman jump - showing at least five spades, and five cards in the suit bid, and a good hand (with a weaker hand simply overcall 2), e.g. KQxxx x AKQxxx x
Notice that there is no way to show a balanced 12-15 points. Indeed - simply pass on these hands. Whilst it is true that you might miss game, they have preempted you, and inevitably bidding is not going to be as accurate as before. What about xx Q10xxx AKx AQx? Pass - and hope that partner can make a take out double, which you will gleefully pass for penalties. Even if partner does not double, it may well be better to defeat 2 undoubled than to try to enter the fray.
If they open a three level preempt, things are much the same, but a level higher. You might want an extra point, but it is worth assuming that partner has a seven count, and bidding accordingly. Similarly, when responding to partner, bear in mind that he is already hoping for you to have a seven count, so don't be too eager to raise him. The main difference over a three level preempt is that the cuebid is now a little pointless as asking for a stop, and so should show two five card suits, and a good hand. Similarly all suit bids will be natural.
Multi 2 opener
If somebody opens a transfer preempt against you, or more specifically a multi 2 (showing a weak two in either major or a strong hand), the principles will be broadly the same, but with some extra options available to you (this is why it is sometimes said that it is easier to defend against a multi 2 opener than a natural weak two bid).
The key bid is double - this should NOT be a take out double. It should instead show 13-15 points with a balanced hand, or a very strong hand. The latter will take care of itself. The former is using the extra space to describe itself to partner by doubling a contract that opponents are unlikely to be able to play in (if you doubled a natural preempt to show this, too often you would force your partner to bid when it would be better to defend). Thus
X: 13-15 balanced, or a strong hand. If the next hand passes (which should show diamonds, though many do not play it this way), your partner should generally pass also, unless he has something to say.
All other bids are natural. If you pass, then you then will bid as before. For example, with Kxxx x AJx KQxxx you will pass, and when the expected 2 comes round to you, double for take out. Similarly, 4 should show clubs and spades. If you pass, and then protect with a suit bid, this should be weaker than bidding immediately.
Harder is bidding once it has started 2-P-2. My advice is pretend it has been a weak 2 opener, and defend as above, with the exception that 3 should be natural.
The only bid that should be different against a multi is four of a minor. There is very little need for this to be a strong hand, since there are plenty of other ways to show this, and going past 3NT may not be wise. Similarly, as you do not know the suit yet, a Roman jump is not so easy to play. My advice is that this is the one sequence where you should preempt against a preempt. Since they don't know what the suit is, this can be a good time to retaliate, and make opponents' life difficult.