The most common method of wort separation is the lauter process. The entire mash is pumped into the lauter tun, a tank with a perforated plate, called a false bottom, acting as a strainer. Liquid is allowed to flow from the bottom of the tank. The false bottom holds up the grain. The wort is pumped out the bottom snd back in the top of the grain bed until it runs clear, a procedure called vorlauf. The bed of grain acts as a filter to clarify the wort. The clear wort is the pumped into the kettle. As the liquid flows out, hot water is sprayed in to rinse additional sugar from the grain, a procedure called sparging.
Most lauter tuns are equipped with rotating knives that can cut into the bed of grain to make flow easier. In some smaller breweries, the functions of the wort separation and mashing are accomplished in a single vessel.
This topic is covered in The Chemistry of Beer: The Science in the Suds, Chapter 8.