What can cause a fast heartbeat and dizziness?

Lots of things. Anything from anxiety or dehydration to a serious abnormal heart rhythm. A fast heart rate and dizziness is something that should be evaluated right away, unless you know it's due to anxiety or it's from dehydration that you can fix by drinking fluids. It can be useful to measure your heart rate and to find out whether it's regular and steady, irregular with a pattern, or completely random.