This is a very concise summary. More info on SAYC: ACBL SAYC System Booklet (PDF format). See also: Full SAYC convention card by Michel Heger and SAYCBridge.com, for online practice bidding with SAYC.
Standard American Yellow Card (SAYC)
opening characteristics response meaning continuation
1♣ 3+ cards 2NT 13–15, GF 
3NT 16–17  
1 4+ cards or 4432 as to 1♣
1 5+ cards 1♠ 4+ spades, 6+ pts, usu. no support  
1 NT 6–9; denies 4 spades or 3 hearts may be passed
2 ♣/ 10+, 4+ cards promises another bid unless passed hand or game bid
2NT ! Jacoby: raise, 13+ 3♣//♠ shortness, 4 min, 3NT med, 3 max
3 limit, 10–12, 3+ hearts (preempt over X) 
3NT 15–17 hcp, balanced, 2 card support  
4 usu. 5+ hearts, shortness, <10 hcp  
1♠ 5+ cards cf. to 1
1NT 15–17 hcp balanced (may contain a 5-card suit, even a major)
2♣ non-forcing Stayman, usu. 8+ hcp 2 //♠ (2 with both majors); responder’s 3♣/ slam interest
2 !Jacoby transfer to hearts 2 , or 3 with max.
2 !Jacoby transfer to spades 2 ♠, or 3 ♠ with max.
2♠ !transfer to 3♣ resp. rebid 3 signoff
3♣/ !inv. to 3NT with 6+ card suit  
3/♠ 6+ card suit, slam interest  
4♣ Gerber, asking for aces 4 = 0 or 4, 4 = 1, etc
4NT natural, invites 6NT  
2♣ strong artificial, 22+ or playing equiv.2 artif., may be waitingopener’s suit rebid forcing to 3 of his major or 4 of his minor; after 2 NT rebid: Stayman, Jacoby, Gerber
2/♠, 3♣/ natural, GF, 5+ cards, 8+ pts  
2NT balanced, 8 hcp  
2//♠ 6+ (or 5) cards, 5–11 hcp; usually no major side suit 2NT forcing, game interest with min. (5–8 p): rebid the suit; with max.: new suit (shows A/K) or 3NT or 4 of minor (shows 4–5 cards with at least Q)
any raiseto play
2NT 20–21 hcp balanced, may contain 5-card suit3♣ Stayman  
3/ !Jacoby transfer 3/♠
4♣ !Gerber 
4NT inviting to slam in NT  
3NT 25–27 hcp balanced4♣ !Stayman  
4/ ! Jacoby transfer 4/♠
3/4 of suitpre-empt, rule of 2/3/4

Choosing the opening

Continuation

Slam conventions

Effect of interference

Defensive bidding

Competitive bidding

Leads and signals