When partner opens 1NT (12 - 14) you will hold one of three types of responding hands:
1) A hand that DOES want to be in game (13+)
2) A hand that MIGHT want to be in game (an "invitational" hand: 11 - 12)
3) A hand that does NOT want to be in game, (less than 10)
1) (a) With a 4 card Major (H/S) you bid Stayman first and then rebid 3NT, 4H or 4S.
(b) With a 5 card - or longer - Major you bid the suit BELOW (a transfer), partner completes the transfer, and then you bid game: With 5 cards you rebid 3NT. With 6 cards rebid 4 in that Major.
(c) With no four card Major you just raise direct to 3NT
2) (a) With 11- 12 HCP and a 4 card Major, after bidding Stayman first, you will only rebid 2NT, 3H or 3S.
(b) With a 5 card - or longer - Major you transfer as before. If you have 5 cards you rebid 2NT. With 6 cards bid 3 in that Major
(c) With no four card Major you just raise direct to 2NT
3) In general ALL these hands will pass. The only time you will bid is when you have a (goodish) 5 card Major and a singleton OR any hand with a 6+ major. In both cases you make the relevant transfer and then just pass. The idea is that you don't want to be in game but you do want to suggest either a lead if the opponents steal the contract later, or a place to play that might be safer than 1NT. You might also talk the opponents out of bidding which is always a good idea! You might also try Stayman with a void or singleton Club, as you can then pass any bid by opener.
So after a 1NT opening from partner, you will either:
BID 2NT or 3 NT
bid Stayman or Transfer and then bid game
bid Stayman or Transfer and then invite game
bid Stayman or Transfer and then pass.