[maris oren]

A to double showing a lot of points-how many points do you need? what shape hand?

[DavidKok]

Takeout doubles show either hands with a desire to compete but no own suit to bid(/no desire to bid our own suit), typically promising support for every unbid suit, or a hand too strong for a direct overcall.
The strength of both is subject to partnership agreement but doubling with a 4441 shape (after the opponents open your singleton) can be done on as little as 10 HCP, and you need a little bit more if the opponents preempted the bidding.
The strong hands usually begin around 17 HCP or so, although the modern expert trend is to allow for heavier and heavier overcalls to get the shape across immediately. In that case the cutoff is a little bit higher. There is no shape requirement, you will clarify shape (balanced or a long suit) on the next round.

[apollo1201]

Where I live, we call this type of X an « all distributions » X so you don’t need specific shapes, but only a big strength. If partner doesn’t convert the X to penalties, you’ll be able to express your hand at your 2nd turn.

By Xing, you think you’ll be handle all what partner could answer, or opps.

How strong? just above the max you allow for an overcall. So the number of points will depend on your partner's hip agreements.

For instance:

(1C) X (-) 1H
(-) ?

1S - 5+ cd, 18+ (usually)
1NT - stopper and better than a NT overcall (19-20 maybe)
2C - cue bid, probably even stronger hand (20+ maybe)
2S - 6+ cd, a bit like a « strong 2 » (but not GF)
etc.

[pescetom]

It's also fairly common that TO double of a major suggests or even promises 4 cards in the other major, unless strong.
Some also play that TO double of a minor promises at least 4-3 in the majors, although this leads to some heavy passes and puts pressure on partner.

[mycroft]

At a beginner level, I would be fine teaching "you don't double because you're 'too strong to overcall'." Not optimal, but don't care, it's better than most other "beginners can understand" answers. Unfortunately, they will learn otherwise from the players in their group, so I at least want to protect them from the really bad ideas (like "double on all 13+").

So:

• If you have a hand too strong to overcall 1NT (so *good* 18+), double and bid NT.
  
• if you have an unbalanced hand, at least that strong (not 18 HCP, but "could miss game opposite a card or two"), you can double and bid your suit. Don't do that with two suits, though; just bid them both.
  
• Otherwise, you have support for all unbid suits - at least all unbid major suits, and "for beginners", let's make it all unbid minors, too - Qxx or xxxx or better. You will by necessity be short in opener's suit; the shorter you are, the less high card strength you need. As others have said, with a perfect 4441 and no wasted values, 1a decent 10 is fine. With a 3=4=2=4, especially if the spades aren't great, maybe start at 12, 13?

Note: this relies on the opponents doing the right thing - including "Centre Hand Opponent" (partner). The reason you need to have "double and bid" so strong is that they do tend to not do what you want - 1♦-X-3♦-p; p and now what? Or 1♦-X-p-2♠; p and you have hearts. Partner's got strength, but which suit to play in?

More specifically for partner, it is critical to have a good idea on the responses. I am a little more aggressive than mainstream, I think, but a pretty standard set:

• 0-8, bad 9: bid the cheapest suit you can play in. The worse you are, the less you need for "play in", in case you get doubled and partner has a better idea.
  
• In particular, partner wants you to pick a suit, she does not want to hear NT from you. Don't bid 1NT just because you have opener's suit stopped, or even because it's your best suit. It will not play well without some cards - so good 6-9 or so.
  
• Good 9-11: jump in a suit you can play in. Because partner might only have Qxx, it's best if you have 5 of them, but you don't want to be 1♠+4 for 200 because you didn't tell partner you had cards.
  
• 12+: cuebid GF. Try to find your good game before you bypass it. Note that cards in opener's suit, especially the Q or J, are likely to be useless, so don't count them in your 12+. The K you can discount, but it's not waste paper; the A is good, but you'd still prefer it in a suit you can develop tricks in.

Now that you see all of that, you can see why the "double and bid" can afford to be "really strong"; you're not going to miss game with a basic 15, 16; partner will let you know if you have enough cards. Opposite 1♦-X-p-1♠; p-, 2♠ is a heavy invitation - good 16, 17 or so - because partner could have zero, and can't have 10. So you have all the tools you need.

Obviously, shape rules, especially in takeout double auctions, and anybody who just blindly follows HCP is going to be behind those who visualize better. But a good agreement that both members of the partnership have will save you from concerns of "but partner doesn't know I'm *this* strong", and won't leave you in the lurch when things get competitive and you haven't shown your suit yet (unless your hand is strong enough that you aren't in the lurch!)