There are probably about three main approaches to this; fly sparging, batch sparging and no sparging.
As mentioned previously, fly sparging sprinkles clean water in at the top of the grain bed whilst drawing off wort at the bottom, batch sparging is similar except you bung the clean water in in batches and stir it up before drawing off the wort. Both of these need some means of filtering the wort out whilst leaving the grain behind - in that link of yours its the stainless braid in the mash tun, other people use slotted copper manifolds or plates with holes drilled in or other kinds of mesh. I've even seen it done in a mesh bag and using a watering can, though it looked a bit tedious.
The no sparge method is a bit different, in that you mash the grains in ALL the liquid you'll use, so its a much thinner mix. This can be done in a big mash tun but typically its done as part of the Brew In A Bag process in one big boiler, and so the grains are lifted out from the wort afterwards in their net bag rather than visa-versa.
As well as rinsing the grains through, the sparge is supposed to be warmer than the mash - this helps rinse out the sugars more easily and kills off the enzyme activity - yet not so hot as to extract tannins and so on. In fly sparging and batch sparging you simply use warmer water to sparge with, with the no-sparge method you would tend to do it in the boiler and heat and stir the grain for a bit after the mash.
Cheers
kev