Standard American Yellow Card (SAYC) is the basic 5-card major system that most beginning duplicate bridge players in the USA play. The system is based on 5-card majors, strong notrump (15-17 HCP), Jacoby Transfers, 2/1 forcing one round, 2 strong artificial and forcing, weak two and three level openings, etc...
Here is the ACBL official description of SAYC(.pdf)
Systems: 2/1 Game Forcing
2/1 Game Forcing systems combine 5-card majors with two-level responses forcing to game. This means that responder must find other ways of dealing with invitiational hands. The common approach is to use 1N as forcing (or semi-forcing) allowing for a large variety of different hands and HCP. 2/1 Game Foricng systems allow for natural bidding and creating game forcing auctions with much space available below game. 2/1 systems often allow for exploring slam without going past game. This is a powerful advantage over the SAYC!
Systems: 4 card Majors
4-card major systems open 1-major with only 4+ cards. There are many different types of 4-card majors. The main differences in the system has to do with which suit to opened when holding more than one 4-card suit. 4-card majors are often combined with strong club systems to provide a strong combination of natural bidding and "efficient use of space."
Systems: Strong Club
Strong Club Systems use 1opening bids as strong artificial and forcing. This allows for more efficent use of space for game and slam bidding. Strong Club systems have several different types, varying in things such as HCP required to open 1, limited HCP for other bids, multiple meanings for 1 opening (Polish), and different response structures.
Systems: Weak Notrump
Weak Notrump Systems are built around the idea of opening 1N with minimum opening balanced hands (11-14 HCP.) Thus, with strong notrump hands players must open a minor and rebid 1N (showing 15-17 HCP.) Weak Notrump Systems are often combined with Strong Club Systems or 4-card Majors to make a complete method.
There are many other types of systems, including forcing diamond, 1-level forcing, forcing pass, and more... The important thing about playing against these systems is to ask your opponents to explain the meaning of their bids.
Systems: System Outlines from Top Partnerships
Meckwell WBF Convention Card