LOOKING FOR SLAM:
OK, there will be times you look at your hand and think, "I must be dreaming," right before your partner opens 1NT. It's pretty easy under those conditions to find slams and grand slams, but when you just can't be sure about points or specific cards, you can turn to a couple of handy little conventions for a little help.
Blackwood:
Sometimes you and your partner will have hands that seem to beg you to consider slam in a suit, but how are you going to find out whether or not you have the necessary strength to go there? Here is where a convention called Blackwood helps out.
Let's say you open 1S, and your partner responds with 3S. Looking again at your hand, you note that you have 19 HCP and five good spades (for the sake of argument, they include the AKQ). Now you know that you have at least an 8-card fit in spades and a bare minimum of a solid 29 HCP. With a little extra information, you may discover that you have enough for a slam, though grand slam is probably out of the question. Normally the auctions that lead partnerships to look for slam are even stronger, but this should serve our purposes well enough.
In this situation, consider bidding 4NT. Why 4NT? We use this bid because it can serve no other purpose in this auction. Game in NT is 3NT, so it can't be a bid for play. Slam doesn't kick in until 6NT. You and your partner have agreed on a suit, so your 4NT bid is too high to be of any real use as a natural bid on the way to finding game in your suit. In this case it asks your partner how many aces he has. His responses are specific: 5C means either 0 or 4 aces, 5D means 1, 5H means 2, and 5S means 3. You should know, after that response, precisely how many aces you have between your two hands. If you are wondering how you will differentiate between the two meanings of 5C, just remember that something has driven you to look at slam, and if you have no aces, 5C had better mean your partner has all four of them; if neither has any aces, your partnership is missing 16 HCP just in the aces.
If, after getting that information, you decide to stop, you can sign off where you need to be by placing the contract at the appropriate level. However, if you are interested in grand slam possibilities (you should have all of the Aces between your two hands in this case, though voids can alter your calculations), bid 5NT, which asks for kings. The responses to 5NT are the same as those for 4NT except that they indicate kings and are one level higher. That is always enough to place the contract with reasonable security, assuming you have not made a gross error along the way.
You should take note of two things. First, Blackwood is not a convention for finding good slams so much as it is a convention for keeping out of bad ones. Use the information to keep from going too high in the bidding. Second, never bid Blackwood unless you are prepared to accept any answer your partner may give. If you are looking for slam in clubs but don't want to go there unless your partner has at least two aces (let's say you are holding one), you will be in hot water if he has one, and thus bids 5D, forcing you to to a slam contract at 6C.
There are a few variations on Blackwood that you may want to look into as you develop your bidding system. These variants allow for greater precision, but you are better off leaving them alone until you have some experience with slam play and can evaluate how each one might fit within your partnership agreements.
Gerber:
Sometimes your partner delivers slam opportunities in NT contracts, and Blackwood doesn't work (his 1NT followed by your 4NT has a special meaning, and it can never be Blackwood). For this reason, we have another bid named Gerber. Let's say your partner opens 2NT. Considering his 20-21 HCP and your hand with reasonable points (let's say 12, just to put the total on the line), you may be interested in slam (again, grand slam is unlikely), so you bid 4C. As with Blackwood's 4NT, this is a bid that can have no other constructive meaning, so we use it to ask for aces.
The beauty of Gerber is this: once you have learned Blackwood, you know Gerber. The responses, relative to the ace-asking bid, are the same. Thus, 4D means either 0 or 4 aces, 4H means 1, 4S means 2, and 4NT means 3. Likewise, you can ask about kings by pursuing 5C and adjusting one level for the responses.
All of the same caveats apply to Gerber as they do to Blackwood. Don't risk getting in over your head. Remember that you are trying to stay out of trouble, not trying to get into a slam. Use these sparingly, and when you do employ them, pursue the results with confidence.
Quantitative Slam Invitation:
In addition to Gerber, there is one other way to chase down a good slam contract quickly. In response to a 1NT or 2NT opening bid by your partner, 4NT says that you have the HCP and distribution for a slam (6NT) if your partner has a maximum opening hand for his level (17 HCP for 1NT or 21 HCP for 2NT). With a maximum opening, he will bid 6NT, and with any less, he will pass.
Similarly, if you are interested in grand slam, assuming your partner has a maximum NT opening for his level, bid 6NT (this contract should be safe, even if he is minimum). He will pass with less than maximum or bid 7NT with a maximum.
While Gerber is handy for finding slams in NT auctions, Quantitative Slam Invitataions save room in the auctions to which they apply. Furthermore, they give less information to you opponents. If you end up in 6NT with one ace missing, you may be able to make the contract before they can effectively attack the suit with the missing ace, possibly giving you time to secure a shaky contract.