"They have the same father."
Translation:Ze hebben dezelfde vader.
In the way it's used in this sentence, it's pretty simple hetzelfde for het woorden and dezelfde for de woorden, e.g. Ze hebben hetzelfde vadertje.
But...there also is a different usage of hetzelfde, when it can be replaced by gelijk or eender (or by equal in English) see the explanation by myself and Simius here. BTW this other usage doesn't apply to the sentence of this discussion, since "They have equal father." is not a valid sentence.