This is really important material. Herbal supplements and even herbal teas, including some marketed and consumed as beverages, can be potent medicines, and like any kind of drug, they can interact with each other and with synthetic pharmaceuticals as well.
Just as a good doctor checks for drug interactions and side-effects, a good herbalist must check for interactions between herbs and between the herbs and any drugs a person is taking.
It's also important to let your doctor know what herbal supplements you use or what herbal teas you drink, as well as informing them about your diet, since drugs can interact with foods as well. Unfortunately, there's not enough research to comprehensively understand all herb/food/drug interactions--and new ones are constantly being discovered. Many potentially dangerous drug interactions (such as the family of drugs which interacts with grapefruit juice) were only discovered by accident.
I think the best solution is to be cautious and sparing in your use of medication, whether synthetic or herbal. Just because a drug has been approved by the FDA does not guarantee it's safe. If it's not medically necessary to take a drug, you should avoid taking it. And when seeking herbal supplements or medicinal teas, try to limit yourself to using herbs that have been firmly established as safe for long-term use, and consult a doctor and herbalist when in doubt.