There are many different types of birth control
pills but they all use some combination of estrogen and progesterone. They work by inhibiting the release of hormones that cause ovulation. They do this by tricking the body into thinking that it already ovulated. Birth control pills have been used for many many years and the ones used today are the safest they have ever been. The pills today use the lowest dose of hormones possible and therefore have the fewest side effects. For most women, the advantage of having a very reliable birth control method outweighs these downsides.
The downsides of birth control pills are that they do slightly increase your risk of developing a blood clot. This is only really significant in women that have a history of blood clots, or those that smoke and are over the age of 35. There is also a slight increase risk of breast cancer, but a slight decrease risk in ovarian cancer seen with birth control pill use. Besides these small risks, there is no permanent damage that these pills induce, nor is they considered bad for your body.
I suggest that you schedule an appointment with your primary care physician
or OBGYN (whoever you go to for your feminine health). He or she can discuss the pros and cons of each method so that you can develop your own plan for birth control.