How are neurotransmitter receptors discovered? Many neurotransmitter receptors are known, for example 5-HT2a, Mu, NMDA, and so on. How have these receptors been discovered?
Each receptor has its own story of discovery. I'll share here the methods used by Lefkowitz that led to the discovery of one of the first neurotransmitter receptors, namely the β2 adrenergic receptor (β2AR) from frog erythrocytes in 1981. With this I mean β2AR was among the first receptors that was identified, purified, and characterized both at the protein and DNA level.

Lefkowitz's team was the first to uncover the charactistics of a neurotransmitter  at the protein and DNA level. βARs are involved in regulating cardiovascular function. Lefkowitz was awarded the Noble prize for his early pioneering work on the discovery of these receptors. 

His method was based on several steps, namely:


The development of a novel and specific radioligand binding assay to enable the measurement βAR-binding sites;
The identification of detergents to successfully solubilize a functional βAR from membrane preparations;
The synthesis of an affinity resin and photoaffinity ligands to facilitate receptor purification;
Reconstitution of the purified β2AR into phospholipid vesicles;
The demonstration that β2AR couples to, and activates the heterotrimeric G protein Gs and subsequent activation of adenylyl cyclase to produce cAMP;
Purified hamster β2AR was used for peptide sequencing that were subsequently used to synthesize oligonucleotides for cloning studies to isolate β2AR cDNA;


After β1AR, Lefkowitz's lab soon purified β1AR, α1AR, and α2AR.

References
- Benovic, Cell (2012); 151(6): 1148-50
- Lopez-Munoz &amp; Alamo, Neural Transm (2009) 116: 515–33