Analog video signals (Composite) use 75 ohm coax cable for transport, so you must match this impedance with a 75 ohm resistor to GND at the input side.
There you can connect the analog switches with their ON resistance between 60 and 300 ohm, depending on the chosen chip.
Finally you must again provide a line driver with an output impedance of 75 ohm. This is typically implemented using a video capable high speed OpAmp with a gain of 2 and a series resistor of 75 ohm feeding the output cable.
The gain of 2 is needed because the series resistor and the cable impedance form a voltage divider and so you have the original input voltage again.
The video path is DC coupled, this is important to provide the correct black level and allow correct sync separation later.
Here is a pre 2000 example of a cheap 16 channel AV switch board, the input resistors are not shown here, they are on another board. The audio inputs have 620 ohm resistors to GND and no amplifier.