When studying gene expression, there are several methods to look at the various stages. In eukaryotes these include:
1-The local chromatin environment of the region can be determined by ChIP-chip analysis by pulling down RNA Polymerase II, Histone 3 modifications, Trithorax-group protein,Polycomb-group protein, or any other DNA-binding element to which a good antibody is available.
2-Epistatic interactions can be investigated by synthetic genetic array analysis
Due to post-transcriptional regulation, transcription rates and total RNA levels differ significantly. To measure the transcription rates nuclear run-on assays can be done and newer high-throughput methods are being developed, using thiol labelling instead of radioactivity.
3-Only 5% of the RNA polymerised in the nucleus actually exits, and not only introns, abortive products, and non-sense transcripts are degradated. Therefore, the differences in nuclear and cytoplasmic levels can be see by separating the two fractions by gentle lysis.
4-Alternative splicing can be analysed with a splicing array or with a tiling array (see DNA microarray).
5-All in vivo RNA is complexed as RNPs. The quantity of transcripts bound to specific protein can be also analysed by RIP-Chip. For example, DCP2 will give an indication of sequestered protein; ribosome-bound gives and indication of transcripts active in transcription (although it should be noted that a more dated method, called polysomefractionation, is still popular in some labs)
6-Protein levels can be analysed by Mass spectrometry, which can be compared only to quantitative PCR data, as microarray data is relative and not absolute.
7-RNA and protein degradation rates are measured by means of transcription inhibitors (actinomycin D or α-amanitin) or translation inhibitors (Cycloheximide), respectively.
References:
Cheadle C, Fan J, Cho-Chung YS, Werner T, Ray J, Do L, Gorospe M, Becker KG (2005). "Control of gene expression during T cell activation: alternate regulation of mRNA transcription and mRNA stability". BMC Genomics 6: 75. doi:10.1186/1471-2164-6-75. PMC 1156890. PMID 15907206.
Jackson DA, Pombo A, Iborra F (Feb 2000). "The balance sheet for transcription: an analysis of nuclear RNA metabolism in mammalian cells". FASEB Journal 14 (2): 242–54. PMID 10657981.
Schwanekamp JA, Sartor MA, Karyala S, Halbleib D, Medvedovic M, Tomlinson CR (2006). "Genome-wide analyses show that nuclear and cytoplasmic RNA levels are differentially affected by dioxin". Biochimica Et Biophysica Acta 1759 (8-9): 388–402. doi:10.1016/j.bbaexp.2006.07.005. PMID 16962184.
Why not use RNAi or CRISPR to knockdown or knockout your receptor? I am guessing you are asking about regulating their expression in cells...Otherwise for GPCR you could use specific inhibitor but it all depends on what you are trying to study.