From my understanding, in RT-PCR we start off with an mRNA molecule, use the enzyme reverse transcriptase to create a cDNA copy (hence creating a double-stranded mRNA / cDNA hybrid), degrade the mRNA, and finally create a complementary strand to the cDNA with a DNA polymerase. If we're ultimately creating DNA and it's being duplicated at each cycle, how are we able to deduce the original quantity of mRNA in our sample? It seems like we would need to combine it with some other method, but a lot of sources I'm seeing seem to imply that RT-PCR alone is enough to "quantify" the amount of mRNA in a sample. Any thoughts on this are welcome
There might be a confusion of terminology. There is real-time quantitative PCR, which can sometimes be called RT-PCR. There is also reverse-transcriptase PCR, which is also confusingly called RT-PCR. To try to reduce confusion, real-time quantitative PCR is also called RT-qPCR or qPCR.
What you describe in your question is the reverse-transcriptase type of PCR. This is used for amplification, not quantification, of starting material.
QPCR or quantitative PCR, on the other hand, uses fluorescent dyes to measure the amount of amplified gene product. Standards provide a baseline measure of how much genetic material you should expect to see over time, at each PCR cycle, for a given amount of measured fluorescence. Measuring fluorescence of your own sample over time, and comparing it against the standard, gives you an estimate of what you started with, initially.
I just wanted to elaborate on the previous answer regarding the confusion between real-time (quantitative) and reverse-transcription(RT) PCR. RT-qPCR refers to real-time quantitative PCR, but some organizations refrain from any reference to quantitation (because it's really only semi-quantitative), instead using the nomenclature rRT-PCR (reverse transcription real-time PCR, I guess). In either case, this technique is theoretically capable of quantification of mRNA copies using the appropriate assay design and standards.
The general principle is that, after the cDNA is reverse transcribed from RNA, it is amplified similar to a normal PCR reaction. This can be accomplished in a single reaction with master mix containing both the reverse transcription and qPCR reagents, or in two separate reactions, by first performing an RT first, and then a standard qPCR on the resulting cDNA. The all in one method requires fewer reagents and less hands on time, but it can be difficult to optimize both reactions at the same time.
Here's a good primer on qPCR assay design. As stated in the previous answer, the quantification comes from some measure of fluorescence related to the amount of amplification product present. In an optimized reaction, the number of amplicons should double with each cycle, allowing for quantification based on how many cycles it occur before a specified fluorescence threshold is reached by each reaction well. Intercalating dyes like SyberGreen quantify total DNA present, whereas fluorescent probes are more specific to your gene of interest. Because it's only semi-quantitative, a standard dilution series of known concentration is included on each plate and used for quantification. The standards should be of the same material and sequence as your gene of interest (DNA or RNA) and should be diluted into a range of concentrations that will likely include the concentration in your experimental samples. You also need to be careful about the possibility of degredation of your standards, as the quality of your quantification is entirely dependent on the quality of your standards.
An alternative approach is to quantify a gene of interest relative to some reference gene that is constituatively expressed at the same level regardless of the experimental sample. This method (sometimes called the delta-delta Ct method) eliminates the need for running a standard curve, but requires additional reactions or multiplexing, in addition to identifying a stable reference gene with primers and possibly probes that will work under the same thermocycling conditions as your gene of interest.
A third option is absolute quantification via digital PCR (dPCR). One issue with qPCR in general is that, even when running samples in duplicate or triplicate, it can be hard to confidently resolve differences in quantification smaller than about 3-fold. Enter absolute quantification. dPCR works by dividing up the reaction into tens of thousands of nano-liter sized compartments, such that each compartment may or may not contain an actual copy of your gene of interest. Fluorescence is only used at the end of the reaction to determine whether each compartment has amplified or not (hence digital, each compartment is a 1 or a 0). Quantification is calculated by determining the ratio of positive to negative compartments and comparing to a Poisson distribution for discrete probability distrubutions. It can have much finer resolution than qPCR, supposedly capable of reliably detecting a 1.2-fold difference in concentrations, with the trade-off that it has less dynamic range with reduced confidence in quantification estimates near the top and bottom of that range. Plus the entire system is usually much more expensive at just about every level (equipment, reagents, and consumables). But with most gene expression assays, you really need to ask yourself if a 1.2-fold change in transcript level is even going to be meaningful in your biological system.