Response to NT openings
The most common is Stayman developed in 1930s, that now has a number of variations and frequently used with an alternative of transfer bids.
The most common variation is for Responder to bid 2C over partner's opening 1NT (or 3C over 2NT).
Opener then responds with:

• 2D - denies a major with 4 or more hearts or spades
• 2H - 4 or more hearts (may also have 4 or more spades)
• 2S - 4 or more spades (denies 4 or more hearts)
• NOTE that the majors are bid in sequence not by length or value so Hxxxx would be bid in preference to SAKxxx

To complement the Stayman convention, many players also use transfer bids over the 1NT or 2NT opening.
Responder bids a suit at the next level (excluding clubs as this is reserved for Stayman) and opener is forced to bid the next suit regardless.
Providing Opener has a good suit in the suit to which the transfer is to be made, probably 4 or more cards with 2 honours, Opener may jump bid, indicating support but it must always be in the next suit above that called by Responder. A jump bid should be used rarely as Responder has 'taken control'. Opener has given Responder a comparatively accurate point count and described the distribution with the NT opening so normally it would be up to Responder to continue the bidding if the combined point count suggests that it should continue. Opener has no idea at this stage, of the point count of Responder.

It is common for players to restrict transfers to 'transfer to majors':
e.g. 2D response demands Opener to bid Hearts, 2H response demands Opener to bid Spades.
However an extension to this will allow a full transfer
e.g. 2D -> Hearts, 2H -> Spades, 2S -> Clubs, 2NT -> Diamonds
Similarly for responses over the 2NT opening.

The one apparent issue with the full transfer is that 2NT can no longer be bid as an invitation to game (or 3NT over 2NT as a 'shut-up' in game. This is easily overcome by using Stayman. 2C -> (any response) -> 2NT. This sequence uses Stayman as an intermediate forcing bid, allowing Responder to bid 2NT (or 3NT if Opener originally opened 2NT).
2NT -> 3C -> (any response) -> 3NT is normally forcing Opener to pass.
The advantage of transfers over weak take-outs, is that if responder is weak, the stronger, opening hand becomes declarer and the weaker hand becomes dummy. Although the responder may have more trumps, there will also be an advantage in responder being dummy as then opener's hand is hidden and defenders will not know how many of the trump suit are in declarer's hand (albeit normally a minimum of 2 as the opening was in NT).
The above may, at first, seem confusing to beginners as being difficult to remember however using both Stayman and full transfers is comparatively easy to remember as ANY response by Responder at the 2 level is a Convention Bid so there is no need to worry as to whether it is natural or not.

Transfers are especially important when bidding a strong 1NT as with 15 - 17 (or as decided) it is even more important thet the strong hand is hidden and the weak hand is dummy.