Is the following table in 3NF:
Customer(CustomerID, CustomerName, DOB, Phone, Address)
I am specially interested to know if the address field should be in this table or should it be further decomposed.
To give a precise answer about what is in normal form and what isn't requires knowledge of what keys and dependencies are supposed to be in effect. Here we have only attribute names to go on so any direct answer to your question can only be guesswork.
My guess is that the Customer table specified is in 3NF. If CustomerID is the only key and if none of the other non-key attributes are determinants then the table as specified is in 3NF.