What does a multiplexer look like?

Physically a multiplexer usually looks like a box of some sort. More important is what is inside. The inside of a multiplexer contains a switch or switches, a power supply, and the electronic circuits to manage the system.

One link is to informative datasheets for a couple of multiplexer Integrated Circuits from which much can be learned about multiplexer characteristics. There are many, many more kinds of multiplexer ICs.