Refrences:
• Chapter 22 of the book 25 Bridge Conventions You Should Know (2nd edition) by Barbara Seagram, Marc Smith and David Bird
• New Minor Forcing on Bridgebum

Playing standard methods, your second bid over partner's 1NT rebid in each of the following auctions would be considered non-forcing:

or In each case, your actions show a weak two-suited hand and partner may pass at this point if he prefers your second suit. Very convenient - if you have a weak two-suiter. However, what this means is that whenever you have a game-going hand you must leap about. Obviously, jumping the bidding uses up valuable space, and that is not ideal either when you want to investigate which game to play or when you have slam interest. Playing New Minor Forcing (hereafter called NMF) a bid of a previously unbid minor suit over a 1NT rebid is artificial (something like Fourth-Suit Forcing), and asks opener to describe his hand further.
New Minor Forcing is used in these sequences: or or

What do you need to use NMF?

Responder guarantees at least enough values to invite game facing the 1NT rebid, so a minimum of 11 HCP. By far the most common reason for using NMF is that you have a five-card major and would like to know whether partner has three-card support.

Let's say you have:
♠AK853 ♥K64 ♦84 ♣A83

Clearly, you want to play in game. Do you think you should bid 3NT or 4♠? Of course, there is no correct answer to this question. However, in traditional methods there is no sensible way to find out if partner has three-card spade support. Playing NMF you bid the unbid minor (2♦) and he will tell you.

Let's say you have:
♠AK853 ♥964 ♦84 ♣A83

This time you have an additional problem - is partner maximum or minimum for his 1NT rebid? You could make an invitational raise to 2NT, but if opener has a minimum he will pass and you will play in 2NT even when he has three-card support for your suit and a spade partscore would be a much safer spot. Once again, using NMF (2♦) is the answer since partner will not only tell about his spade support, but also whether he has a maximum hand.

Can you use NMF when you have both majors?

You certainly can. Indeed, hands with five spades and four or more hearts can be bid much more accurately using NMF. Consider this problem playing traditional methods:
♠AK853 ♥KJ64 ♦84 ♣K3 Playing NMF, you start by bidding 2♦, your artificial forcing bid. Remember, this bid asks partner to describe his hand further. If he has four hearts he will tell you about them. If he does not, you need never bid the suit. Easy! As a result, when you jump to 3♥ in this auction rather than using NMF, you guarantee a five-card suit. With a weak hand, and four or more hearts, you simply bid 2♥. Partner now has a lot of information with which to make a decision on how high to bid, and in which denomination.

What if both minors are unbid?

There is only one auction that can produce this situation:
♠AJ864 ♥Q6 ♦KJ6 ♣963 Treat a bid of either minor as semi-artificial and forcing for one round. Bid your better minor (usually the minor in which you have a notrump stopper) - on this hand, bid 2♦. Partner will tell you if he has three-card spade support and whether he is maximum for his 1NT rebid. He will also know to avoid 3NT if he also has weak clubs. If your minors were reversed, you would bid 2♣ instead.
A popular alternative is to play that 2♣ is always NMF here, while 2♦ shows diamonds.

What do you do when partner uses NMF?

Having looked at the various problems from responder's side of the table, we now move around to opener's seat. You open the bidding and rebid 1NT. Partner now wheels out his new toy - New Minor Forcing. What do you do? The responses to NMF convey a considerable amount of information regarding shape and strength. They are listed here in order of priority.

Priority 1: Show an unbid four-card major.

This can only be hearts - if you had four spades you would have bid or raised spades, not rebid 1NT. Note that you will often have four hearts when you open a minor and rebid 1NT over partner's 1 ♠ response. You have neither the shape nor the strength to reverse, so you had to settle for 1NT. Now partner asks for more information:
♠K3 ♥KJ85 ♦AJ84 ♣Q84 How many hearts do you bid? As is the case in all of the replies to NMF, you make the minimum bid with a minimum hand, and jump with a maximum. The hand above has 14 points, so you would jump to 3♥. We are calling this hand a maximum because your 1NT rebid shows 12-14 HCP.
Remember that when he uses NMF partner only promises the values to invite game (11 points). He also knows that you may have only 12 points. 11+12 does not sound like enough points for game, so you must jump to show your full-strength opening bid when you are a little better than minimum. If you had a minimum opening bid with four hearts, you would rebid 2♥ only.

Priority 2: Support partner's suit if you can.

♠K75 ♥A62 ♦KJ85 ♣K85 Partner bids 2♣, NMF, over your 1NT rebid. You do not have four hearts, so you can ignore Priority 1. Priority 2 is to show support for partner's suit, which you have here. As before, you are maximum for your 12-14 INT rebid, so you must jump to show this too - bid 3♠. With the same shape and a minimum opener you would simply bid 2♠.

Priority 3: Show your range.

If you do not have an unbid heart suit and cannot support partner, the only thing left to show is your range - maximum or minimum.

When you have a minimum hand, you have two options:
♠86 ♥AQ7 ♦K10975 ♣K106

You do not have four hearts and you cannot support spades. You have a minimum opening bid with stoppers in the two unbid suits (remember that partner's 2 bid was artificial, so only diamonds and spades have been bid naturally). Bid 2NT. If partner has only invitational values, he will pass. If he bids again then you are now in a game-forcing auction.
♠K6 ♥AQ7 ♦K10975 ♣1086 As before, you do not have four hearts and you cannot support spades. You again have a minimum opening bid, but this time you have no stopper in one of the unbid suits, clubs. Rebid your first suit bid 2♦. If partner has only invitational values he will either pass or convert to 2NT. Any other continuation creates a game-forcing auction. Given the chance, you can bid the suit in which you have a stopper.

When you have a maximum, you must force to game since you know that partner has at least an invitational hand. Essentially, you can make any bid that we have not so far mentioned, but you have two basic choices:
♠Q6 ♥AQ7 ♦K10974 ♣K106
This is the same hand as before, but with the Q added to make it a maximum 1NT rebid. You still do not have four hearts, nor can you support spades. However, with stoppers in the unbid suits and a maximum you can bid 3NT.
♠K6 ♥1086 ♦KQ975 ♣AQ7
This time you have a maximum with a stopper in only one of the unbid suits. How you show this will depend on which suits have previously been bid. On the auction above, you can simply show your stopper by bidding the suit you have stopped - 3♣.
♠K6 ♥AQ7 ♦KQ975 ♣1086
Now you cannot bid the suit in which you have a stopper - hearts - as that would show the suit. The answer is to jump in your first suit - 3♦ - to show extra values but a hand that cannot bid 3NT or 3♣. Partner will work out why.

What do you do when you don't have enough to invite to game?

Let's start with the simple situation:
♠KQ863 ♥Q1083 ♦85 ♣72 Clearly, facing a 12-14 HCP hand, you have no interest in game. Since your second suit is hearts, you can just go ahead and bid it - 2♥. Not only does this tell partner you are at least 5-4 in the majors (with 4-4 you would have responded 1♥ not 1♠) but it also tells him not to bid too much. His choices are simple - pass, 3♥, or give preference to 2♠.
We know what you're thinking 'What about when my second suit is an unbid minor?' You don't really want to play in 1NT when you hold a hand like this one:
♠K1063 ♥84 ♦9 ♣QJ9753 You are fairly sure that clubs will play at least as well as notrump and probably much better. However, you do not have the values to invite game, so you cannot bid 2♣ as that would be NMF. What a nasty situation.
The solution is that you can jump to 3♣. This says to partner, 'Please pass and put down dummy. Note that as partner cannot pass a 2♣ bid, you no longer need 3♣ as a forcing bid.

What's your next bid?