The process depends upon where the child resides. If you are all in California there are forms that are filed. If the child resides in another state or another state has jurisdiction over the child you should consult an attorney in that state. Otherwise if the child is in Sacramento, your family court should have a family law facilitator's office that will help you with what forms are needed.
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The agreement needs to be placed in the proper format, signed by the parties with a provision that sets out, It is so ordered with a place for the judges signature. Unless this is set up correctly, signed by the judge and filed with the court it is not an enforceable order. I would hire a family law attorney to prepare the document for you to ensure that you will have an enforceable document without delay.