I have a 2000 vw beetle and the blue water light or tempature light stays on?

Blue light is normal for a few minutes when first starting. Since the Beetle does not have an engine temp gauge it uses this light to indicate cold or hot. If the light stays blue all the time then you likely need a new thermostat. While thermostat is out tech should inspect water pump impeller with a mirror or finger to be sure it is not cracked. If the light goes out after 3-5 minutes of driving then this is normal. The biggest concern is if the light turns red or flashes. In either case pull over and have it towed to a VW specialist.

Do you have the owners manual?