I know that tachycardia results during exercise but when is it dangerous?

Hard to get there. Assuming you are in otherwise good health, the generally accepted max sustained heart rate is 220 minus your age. But many people (see tim noakes' work on the "central governor") will say that your body will stop you before you do damage. Of course, before starting any new exercise regimen you should consult your physician.
If too fast. The heart rate increses in exercise as part of a normal Adrenalin increase, normally 190-200bpm in healthy younger people at peak exercise. As exercise ends, the heart rate falls back to lower resting rates. Persistent rates over 220-250bpm, or irregular with symptoms, especially when they occur without exercise and don't slow down or stop can be abnormal.