It's still a bit of a broad question.
As a general answer, there are basically three types of fabric:
Crossbar Matrix (think of a large Tic-Tac-Toe figure):
A crossbar matrix can logically connect all of the inputs (horizontal bars) to all of the outputs (vertical bars), by applying some hardware or software logic to make the connection at the appropriate intersection.
Shared RAM:
With shared RAM, the input data is parked in a specific buffer area, the proper path is determined in logic, then the egress port(s) are pointed to the data in RAM (CAM) and clocked out to the destination.
Bus (shared connections on a single data path):
The ingress data is buffered, the switching logic determines the egress path, and the appropriate ports are logically connected to the bus and the data is clocked out to each port with a connection.
There are some varients, but all basically boil down to one of these types.
For example, (some) Cisco switches (used to?) send all ingress data to all ports (to a buffer). The switching logic detrmines the proper egress path, then flushes the data from the ports that shouldn't send it. The egress ports are then instructed to pump out the data. (a flavor of shared RAM).
Digital Equipment Corp (DEC) used to market switches with a true crossbar matrix. Nortel's original ATM switch (the 10000) was a pure crossbar matrix. Crossbar is the most eficient and allows the greatest expansion (while maintaining speed), but it's also the most complex and expensive as well as the most logic-intensive.
Most switches these days (I believe) are using some form of shared RAM. It's still pretty efficient, inexpensive, and easy to implement in ASIC (relative to the X bar).
FWIW
Scott
