How do longevity meds work?

No such thing. Although researchers are fast at work, there are no known meds, supplements or herbs that haveever.Been shown to slow or reverse aging. There are two major theories of aging. One says it's all about damage to dna. The other statess it's genetically programmed. Either way, living a healthy lifestyle will help you age normally and gracefully.
Meds? I don't know of any "longevity meds" per se, but there are many agents that can help. What "longevity medicine" boils down to is becoming as healthy as possible. This means a good diet, correct supplements, exercise, and good attitude. There are also a number of herbs, known as tonic agents, that can be helpful. In addition, many therapies can correct problems. Best to see a doctor in this field.