Typically receptor-ligand binding assays are done in vitro, ie the receptors are expressed on cell membrane fragments within a test tube/plate well [cell membrane is the wall of a cell. the way drugs exert their action is by binding to the receptor (attaching to it) which is on the cell wall, which then causes changes inside the cell, which ultimately causes changes in the way your brain handles information. so, in vitro (in the lab), they have the receptors on a piece of cell wall in a dish and add the drug and basicly watch what happens] , however they can also be done with frog eggs are tissues expressing the receptor to get a more realistic determination of the receptor-ligand interaction in vivo [in vivo means outside the lab. using actual biological cells (frog eggs eg) they can see what the drug is doing when there are other factors present] . The ligand is a radioisotope, so once it is added and the reaction mixture is washed of free ligand, the amount of ligand-receptor binding can be determined with a scintillation counter.[the ligand (drug) is a radioisotope, which just means its modified so that it emits radiation. if my interpretation of what he said is correct (not entirely sure..), after they add the ligands and the ligands bind to the receptors (the molecule to be binded to the receptors, ie, the drug) they then wash the rest of the ligands out. what's remaining will be the ligands that binded to the receptors. using a scintillation counter, which is an instrument that measures the radiation, you can determine how much of the ligand (drug) remains (ie how much bound to the receptors) then its just a matter of math to calculate the binding affinity (how much the drug 'wants' to bind to the receptors]
As for any specific experiment, read the methods.