How does the fire department connect to a fire hydrant?

There is a suction line on every apparatus with a pump. The engineer, who drives the rig, connects this line to the hydrant and to the pump suction. Some equipment has this line pre-connected to the pump inlet.

In many fire hydrant systems there is enough pressure to fill and pressurize an ordinary hose (of large diameter) running from the hydrant to the pumper truck's inlet. That way, there is very little "suction" required in the pump, since the water is already being delivered with some amount of pressure.

If it is "dry hydrant" with no pressure, then suction is required.

Edit: Typically it is a Firefighter that 'snubs' the hydrant, not the Engineer. It is the Engineer's job to 'Position' the apparatus before transferring the engine into 'Pump' (typically, once the apparatus engine is transferred to 'Pump', it is stationary throughout the incident). There are different options for water 'Intake', they can be long leads whereby a supply line can be a smaller diameter (2 1/2") or a 'Short Sleeve' (4") direct to pump diameter where the Pumper is 'Positioned' close to the hydrant snubbed. There are also situational logistics which require two Pumpers (or more) to 'Relay' a supply line due to the fact that the total amount of hose on a given Pumper is less then the distance from the fire to the hydrant. It is the Engineer's job to figure out what pressure is incoming from the supply line and the amount of nozzle pressure required for firefighting at the nozzle. This determines what pressure you need to be pumping at. This pumping pressure must take into consideration elevation, friction loss of pressure in the amount of hose laid out, etc. It can be a life or death calculation for the Firefighter at the nozzle's fighting end which could very well be 40 stories above the Engineer manning the pump.