how to determine the signs of a blown head gasket in a 2001 Audi A4 V6 ENGINE

Actually, it could be either, but pulling the radiator and checking that first would be the easiest and cheapest place to start. A radiator shop can pressure check your radiator. If you get a pressure leak through your oil cooler (it will be very noticeable), then throw in a new radiator....flush your cooling system as well as replacing the oil too and you're on your way. If the radiator checks out, then DEFINITELY go to plan b and get a head gasket job quickly before it fully goes and fries the engine.