Roman Key-Card Blackwood (RKCB)

RKCB is used after you and partner have agreed on a trump suit. Your auction must have confirmed support for a suit -- or one of you must have shown great length in the suit -- before you can assume that 4NT is Key-Card Blackwood. This is one of the most difficult aspects of RKCB to handle, so it's important for a partnership to discuss what types of auctions will confirm a trump suit.
If you bid 4NT directly over a 1-level opening bid, it's most valuable to use this as just "regular" Blackwood. No suit has been raised, so opener's response shows only the number of aces.
If you have an agreed trump suit, the responses to 4NT give information about 5 key cards -- the 4 aces, plus the king of the agreed trump suit. The meanings of responses to 4NT are:

• 5C -- 0 or 3 key cards
• 5D -- 1 or 4 key cards
• 5H -- 2 key cards, but no queen of trumps
• 5S -- 2 key cards WITH the queen of trumps
• 5NT -- 2 or 4 key cards AND a useful void
• 6 of a non-trump suit -- 1 or 3 key cards and a void in that suit (this is only used if the void suit can be shown below 6 of your trump suit)
• 6 of the agreed trump suit --1 or 3 key cards and a void in a higher-ranking suit

Finding outside kings

After a 5C, 5D, 5H or 5S response, the Blackwooder can bid 5NT to ask about the number of kings you hold. Since you've already shown (or denied) the trump king, you don't count this when you make your 6-level response to the king-ask. The steps are 6C (no outside kings), 6D (1 king), 6H (2 kings), 6S (3 kings).
If the Blackwooder uses the 5NT king-ask, he guarantees that your side has all five key cards and he promises interest in a grand slam. If you have significant extra strength or an undisclosed source of tricks (a solid side suit, for example), you can accept the grand-slam try immediately (without answering number of kings) by jumping to 7 of your suit.

Finding the trump queen

If responder has 2 key cards, his bid of 5H or 5S will also tell you if he holds the trump queen. You can also get this information after a 5C or 5D response. To do this, the Blackwooder bids the cheapest step (5D over a 5C response, 5H over 5D).
If the Blackwooder uses this step to ask and you do not have the trump queen, you retreat to 5 of your agreed suit. If you do have the queen, you bid the cheapest suit where you have a king.
After you bid your cheapest king, if the Blackwooder has room (and is interested in a grand slam), he can bid a new suit to ask if you have a king in that suit, too.
Here's an example auction:

   AK943                              Q876
   AQ1043                             K5
   A2                                 K1043
   4                                  AJ5 

  Opener:                             Responder:                             
    1S                                 2NT (forcing spade raise)
    4NT (How many key cards?)          5D (I have 1 or 4 key cards for a spade slam.)  
    5H (Do you have the spade queen?)  6D (I have the spade queen AND the diamond
                                         king, but I don't have the club king.)
    6H (I need the heart king.)        7S (I have the heart king, too.)
    Pass (Yay!)

NOTE:

There are several variations of RKCB responses. The "standard" treatments are the 5C, 5D, 5H and 5S responses, and the Blackwooder's use of the cheapest suit to ask about the trump queen. However, some pairs use different responses to show voids and to answer the queen-ask. Also, some pairs bid specific kings (instead of using the steps) when the Blackwooder uses the 5NT king-ask. You should go over these parts of RKCB with your partner to be sure you're both playing it the same way.