Note: this article probably needs a revision.
There are many materials on the internet that describe 2C and the responses. In this document, I hope to describe a relatively streamlined protocol for this convention that may be easier for learners to understand. It is also couched in a way to appeal to logic rather than rote.
When you are very strong, there is a good chance that partner won’t even participate in the auction even after you open a 1 level bid. Therefore, there exist conventions for opening with strong hands in SAYC. 2NT is a well-known convention for describing balanced and strong hands. This document shall not touch on it further except to say that some partnerships allow you to bid 2NT with a well formed 19HCP and balanced, or to bid 2NT with 5 card majors. These exceptions are meant to allow you to get around the problem that partner could pass your opening bid. A 2NT bid is generally a limit bid and can be passed (non-forcing).
2C is a convention for filling in this gap. It either describes a hand even stronger than 2NT (good 22 or 23+ HCP and balanced) or a very shapely and strong hand (19+HCP and 4 losers). A 2C bid almost always will lead minimally to a game or slam and is forcing for at least one round. In this document, I encourage learners of bridge to regard a 2C as forcing to game. The reason is that with a 2C hand, it is common for a makable game to exist – even with 1 or 2 HCP! So to avoid skittishness on the part of the learner, I suggest just treating 2C as game force. By treating 2C as game force, there is no need to jump to show suit length or strength, there is no need to fear that partner will pass below game. This makes bidding easier.
When your partner opens with 2C, she is saying “Partner, I either have 23+HCP and a balanced hand, OR 19+HCP with a shapely hand, having no more than 4 losers. I am likely to have a lot of playing tricks".
EDIT: Please look up Playing Tricks via the link. For a shapely hand, the suggestion is you open 2C with 8.5 playing tricks and above - which is why "forcing to game" is justified.
So there are 2 cases.
(A) When partner has 23+HCP and is balanced. (call it a "Balanced 2C")
(B) When partner has 19+HCP, 4 losers and at least one suit with 5+ cards with lots of playing tricks. (call it a "Shapely 2C")
The response by partner
I suggest the following simplified protocol
(C) If responder has 8+ HCP, and a 5+ card major, bid that major. If responder has 8+ HCP and a 6+ cd minor suit, bid that suit.
(D) Otherwise simply bid 2D. Do not bid 2NT even if you have 8+HCP and balanced. This is the default bid
Note : it is not a good idea for responder to bid 2NT.
The rationale for this follows the need to preserve bidding space. If you have 8+ HCP and a 5 cd minor suit, bidding on 3 level removes bidding space for opener to further describe her hand. See "The rebid by opener".
Generally, the responder is the Captain (see “The Captaincy Principal.pdf”), so hiding the information (case D) from opener is ok.
The rebid by opener
The opener will need to distinguish between case (A) and (B). After a 2D bid by responder, this is easy.
With a balanced 2C opener, rebid 2NT with good 22/23HCP to 24HCP and 3NT with 25+HCP.
With a shapely 2C, rebid your first suit at the cheapest level. Prepare to rebid your first suit (if single suited) or second suit later (if 2 suited). See below.
If responder had bid a suit (showing 8+ HCP and his own good suit), continue to bid NT to show a balanced 2C or a suit to show a shapely 2C opener if you don't have a fit for opener.
If you have 2 suits, don't worry, you can rebid it later since it is a GF. Partner will realise you have 2 strong suits.
if you have one long strong suit, you rebidding it again later shows. Partner will realize you have 1 strong suit. If you are using playing tricks as a criteria, partner will know your long suit is almost as good as a solid suit (and he might bid game in that suit even with 1 or 2 card support).
The whole point is to clearly show if you are a 23+ HCP balanced hand or a shapely hand that is more suited to a trump contract by the second opener bid. By doing it this way, responder has a clear picture of what next to do.
What if opponents interfere?
Responder may choose to
pass (with 0-3HCP). Waiting for opener to bid on to describe their hand.
With good 3/4+HCP, double. You are also waiting for opener to further describe their hand. There is at least a likely game somewhere.
With a long suit (5+) and 8+ HCP, bid that suit. With a good stop in opponent's suit (unlikely), you can bid NT.
In most cases, you are waiting for opener to further describe their hand, similar to if there were no interference.