We've been interested in studying RNA since long before RNA sequencing was developed. Here are two different technologies that are still widely used today:
Quantitative PCR (qPCR)
We can perform a special polymerase chain reaction (PCR) reaction that amplifies RNA from a specific gene. Each cycle in this PCR reaction effectively doubles the number of copies of our targeted gene.
By measuring how many PCR cycles it takes before we can detect these copies, we can calculate the original quantity of RNA from our targeted gene.
Because we can only look at one gene in each qPCR reaction, this method is best for measuring a small number (1-100) of genes.
For qPCR, we used special DNA primers to target a specific gene. Using the same principle, we can design short stretches of DNA that bind to specific complementary sequences. If we attach these short stretches of DNA to a solid surface and then wash an RNA sample over this surface, these short stretches of DNA will bind to and hold RNA from the genes they target. After this washing/binding step, we can calculate how much RNA from the gene we're interested in was in the original sample by measuring how much RNA is stuck to this solid surface.
A microarray contains thousands of different, short DNA sequences attached to a slide or chip in microscopic dots. Each dot contains DNA sequences that will bind to a specific gene. So if we have 20,000 dots on a microarray, each targeting a different gene, we can measure how much RNA sticks to each of these dots and calculate the original quantity of 20,000 different genes in our original sample. This makes microarrays ideal for economically measuring the expression of thousands of genes at the same time.
Further (Advanced) Reading