The double was originally intended to be for penalties. Over time, bridge players realized that it makes no sense to double for penalties at a low level under most circumstances. They then used it for other purposes. I shall group them generically under the name "forcing doubles", as in "forcing partner to bid".
There are actually a lot of types of forcing. All potentially confusing, especially if you try to memorize them all. I'm going to try to take a non-conventional approach and try to unify all these using a logical framework, so that your memory work is much less. I also too lazy to write a description of each haha.
You might want to read this later:
takeout doubles. https://www.bridgebum.com/takeout_double.php
negative doubles. https://www.bridgebum.com/negative_double.php
support double. https://www.bridgebum.com/support_double.php
responsive double. https://www.bridgebum.com/responsive_double.php
reopening double. https://web2.acbl.org/documentLibrary/marketing/VVPTRD.pdf
"Whoa!" you say..... "this is a lot!". Believe it or not it has common denominators.
The most important 3 are takeout, negative and support double. Learn these 3 if nothing else.
for now, we shall assume that "Forcing Doubles" are identified when partner bids a X up to 3 level bid by opponents. A second double is usually a penalty. It is possible for one to covert a "forcing double" to a "Penalty" but this is rare and fraught with mistakes - therefore I shall ignore it.
Try to fit the "General Principles" to the references cited in the introduction. Use the general principles instead of trying to memorise the points in the references.
(A) Ignore the beginner's assertion about 8 card trump fits. At the 2 or even the 3 level, a 7 card fit can be playable. See (E)
(B) You double when you cannot overcall or bid a suit, but are strong enough and shapely enough that if partner rebids in a unbid suit or repeats the partnerships bids, you think you will have a fit (see A) and can play that contract successfully. You do not intend to bid on unless it is to raise your partner's free bid.
(C) You also double when you are so strong that it doesn't matter what suit partner rebids. You intend to bid on after partner's rebid. Your partner can recognize that you are this strong by your rebid.
(D) Partner must respond to a double unless the opponents interfere again after the double.
If the partner is forced to respond (because opponents didn't continue bidding), it is a forced bid. Partner is assumed to have the absolute minimum of points (even 0 pts in the case of a takeout, or 12 pts for opener in the case of a negative double). You will very rarely pass the X to convert it to a penalty - for now I shall assume it is impossible.
If the partner freely bids a suit even after opponents made a bid after the double, it is a free bid. Partner is assumed to have points to respond to your suit constructively (in the case of a takeout at 2 level 6-9 pts).
If partner jump shifts a new suit, he is exploring for game. He probably has enough to explore for game.
(E) Partner is strongly recommended to bid a suit - even a 3 card suit (see (A)). He may rebid his own suit with a 6 carder. NT ONLY if he can't bid a suit and has good constructive values opposite minimum partner strength and strong stops in opponent's suit.
(F) Always prefer a major suit response to a double if possible.