So my ex boyfriend is not my one year old son's real father but he is on the birth certificate. I want him off and to have no rights to my son.
Can I have him just sign over his rights or what do I have to do?

No, in fact it all depends ( if in the US) as to what state you live inl

In a couple states he is the legal father and will remain so, can't be taken off
In some other states, there has to be a legal challenge to his paternity in court. Often by him or the real father.
In some states there is a time limit, after a number of years it can not be challenged.

So you will need an attorney to walk though the laws for your area. Also if you knew he was not the father and had him sign, and he knew he was not the father, that is of course fraud, and another legal issue that can be criminal.