Okay, so genesight is just a brand. It is based on an analysis of your DNA.

What the test actually looks at are "SNPs." These are one letter in a specific gene (A, C, T, G). The SNPs they look at are ones that are different in different people, and identify which version of a gene (allele) you have. They can't say with absolute certainty, but it can check for most of the common variants.

Some of the genes it looks at are cytochrome P450 enzymes. There are a few others I can explain if anyone wants, but I'll keep this to the CYP genes to stay kind of on topic for the thread, and because this explanation is already long and complicated.

Cytochrome P450 enzymes are enzymes in the liver that help break down certain drugs. There are a lot of them, but some meds only get broken down by one or two specific ones.
There is also quite a bit of variation. Some of the enzymes have little to no variation within a population - almost everyone has 2 functional copies. But some, like CYP2D6 (the most common example) show much more variation, with non-functional, less-functional, normal, and extra strong versions all existing and not being super uncommon.
CYP2D6 is also involved in metabolizing a lot of meds, including psych drugs, and is one of the most important ones looked at in tests.

Without getting too much into the chemistry, some meds stop working when they get broken down, some meds have different outcomes depending on how they're broken down, and a few meds only work if they get broken down by these enzymes (e.g. codeine doesn't work for people without functional CYP2D6 because that's the enzyme that turns it into morphine!).

We all have 2 alleles for every gene (except some X chromosome stuff, but that's a weird exception). For a lot of genes, as long as one is functional it will be the same as 2 being functional. But if both of your copies are "broken" versions, then you won't have a functional copy of that enzyme to perform the function.
This matters for psych meds because of the reasons above, whether or not and how they get broken down affects levels of the med and the stuff it gets broken down into.
Meds can also affect the efficiency of the enzymes. Some meds will impair or block the function of certain enzymes. So like Prozac inhibits CYP2D6. If someone was taking codeine and started taking Prozac, the codeine would become less effective because Prozac is inhibiting CYP2D6.
This can lead to all kinds of fun med interactions. A lot of these interactions result in higher levels of the meds in your body, so if I'm on, say, Abilify, and then start taking Prozac, the Prozac can increase the levels of Abilify in my system, and I could start having new or stronger Abilify side effects because I started Prozac.
I might attribute them to the Prozac if I didn't know though. This is why they say not to have grapefruit if you're on certain meds, because it inhibits CYP3A4.

So, you can imagine that variation in how you break down meds and what they're broken down into--some of which have their own effects and are called "active metabolites" and can have different effects than the original meds or other products--will affect which meds might work for you.
I prefer to avoid drugs that are primarily metabolized through CYP2D6 because I have two non functional copies.

But even some SNPs are inconclusive. The test is looking at single nucleotides, so sometimes a certain variation is always or almost always found in people with a nonfunctional copy, but others tend to be found in nonfunctional copies, or mean that you have a less common variation which may or may not be functional.

Whether or not it's a functional version can be determined with sequencing, including gene sequencing, whole exome sequencing, or whole genome sequencing. I got my whole genome sequenced for $500, but unlike Genesight I had to do the data analysis and interpretation myself, and it wasn't covered by insurance. Honestly it's excessive if this is the only thing you want to check, I did it because I wanted to.

So these tests can tell you based on some of these genes that certain meds are more or less likely to work well for you, but it's just one of many factors that goes into whether or not a med will work for you. There are so many more factors we don't understand, it just helps make educated guesses when you're deciding what to try first.

Genesight also looks at SNPs in a few other genes that affect how your brain reacts to meds. Often we're not sure why exactly, but studies will show that, on average, a certain med is much more likely to work in people with a certain SNP. There are a ton of possible explanations, both direct and indirect, but it can at least be used to make better guesses about what med is more or less likely to work.

Genesight or any other genetic test absolutely cannot tell you that any specific med will or won't work for you.
And if you are interested in the most basic analysis, a $100 test (or $60 on sale) from 23andme or AncestryDNA will include most of these SNPs. They're not FDA approved for medical use and don't have that guaranteed level of accuracy, but they are good enough for educated guesses.
I did that before I did whole genome sequencing, and I used a program called promethease that generates a convenient report from your raw data that lists your SNPs including the most relevant ones and does give you some pharmacology interpretation, though you'd want to check with your doc about that interpretation.

Genesight really does help make better guesses about which med to try first. An analysis that looked at different studies showed that

source


The individual studies didn't really have enough data to draw any conclusions, especially about "effect size," but at a glance it seems like the rate of response to the meds based on genesight or not based on genesight, depending on how they measured it and a million other disclaimers and limitations, was about 1.5-2x higher (table six)

This ended up a lot longer than expected. Full disclaimers: not a doctor, not a pharmacist, no extensive training in pharmacology. Basically not qualified wrt human health outcomes, though I have quite a bit of familiarity, and none of this should be taken as health advice without talking to your doc.
(I am a biologist, and I do know about genetics and it's kind of part of what I do for a living, so I would certainly hope I know what I'm talking about there)