If you REALLY want to understand this stuff, then you need to understand that there is no such thing as a COVID test or a COVID test machine.
All of the tests that are being done, are using DNA analysis machines. The exact same machine that is used to do paternity tests or to identify crime suspects.
The only thing that changes when you test for SARS-CoV-2 is that the test kits used have some fragments of DNA that are unique to the novel SARS-CoV-2 strains of Coronavirus.
To begin with, you need to understand DNA, how it is unzipped and transcribed into mRNA molecules, and how those RNA molecules are the program tapes that get translated into proteins by a molecular machine called a ribosome. The resulting proteins are often hormones and enzymes that cause things to happen in the body.
The attached PDF has the very basics for high-school students. You can think of the DNA as program storage on disk, the RNA as an app, and the ribosome as a device in which you can install the RNA in order to run the app and get a result.
The machines that run these analyses all use DNA molecules that have been broken into short fragments. DNA has an up direction and a down direction so they often attach a fluorescent dye molecule to the up end of each fragment to make them visible.
But, there is a problem with retroviruses. No DNA only RNA. Fortunately, researchers have already adapted DNA analysis machines to work with RNA since it is useful for something called gene expression analysis. Simply take an RNA molecule and use reverse transcriptase to reverse the transcription process and get a fragment of DNA as the result. If the DNA is too long, it can be fragmented as mentioned above.
Next step is to amplify the DNA by cloning and making many copies of these fragments.
Then, the fluid containing the fragments is sloshed over a microarray or strip chip, or some paper or plastic strip that has been prepared with probes which are the other half of the DNA fragments you are looking for. DNA molecules are symmetric with two halves for each codon sequence. The DNA fragments naturally stick together, and then something detects the fragments sticking to the probes. Generally a laser scans the strip or chip and in the spots where it glows, you know you have a match. Strong glow means strong match. Weak glow means weak match. The machines do some statistical analysis including comparison with special spots that exist for calibration.
You might want to go through all the handouts and activities for this high-school course.
https://www.affymetrix.com/about_affymetrix/outreach/educator/microarray_curricula.affx