If my 18 year old son’s father died 2 days ago and he is not on the birth certificate but we had a DNA test done when he was born, how would he get share of his father’s assets?

First, bear in mind that if there is a will, your son will most likely get nothing unless he was either named by name in the will or the will states that something is left to "my children" without identifying who they are. A person does not have to leave anything to children: disinherting some or all of them is perfectly legal. So if there is a will, unless your son is named by name or as part of an otherwise unspecified group ("my children") he will not inherit--if other children are named by name, then if you son is not, he will not be included.
If he is named by name, he should inherit, and would file a challenge to the will during probate if he does not.
If there is no will so that, as a biological child, he will inherit, or there is a will not naming children by name but only saying something like "my children," then he will have to 1) file a challenge or "exception" in probate court to the will or the estate's probate and 2) in that challenge, prove (e.g. via the DNA test) that he was the deceased's child.
Note that this is apt to be a complicated legal action--much more so than, say, a small claim suit. While you can help him, your son needs to file this in his own name since is 18 (an adult). Unless you or he have experience with the law or probate, you are advised to retain a probate attorney to help him...which also means that if you don't think his share of the estate is worth enough to pay maybe $10,000 in legal and related fees (e.g. for a DNA expert) while still leaving enough to make the effort and investment worthwhile, it's not worth him taking action.