For this article, I am going to assume that you do not believe you were successful and you want to know what to do about it. You will definitely need to check this article against your state and local civil procedure and appellate statutes and rules, and will probably need to consult an attorney as to your best course of action.
Generally, a decision that is considered a final judgment is appealable to your state court of appeals. To see how to proceed on that, look at your state rules of appellate procedure or contact a local attorney. There are definite deadlines to do this, as well as very specific procedural rules with which you must comply, or lose your right to appeal.
You may also have the right to file a post-judgment motion with the trial judge. Such post-judgment motion usually points out specific errors the judge made (such as excluding an eyewitness to a visitation denial) and asks the judge to reconsider his or her ruling, based on the flaws you are pointing out. This is not the time to argue your case again, nor is it the time to present evidence you should have presented at the hearing. It is the time, however, to argue that the judge made an incorrect decision because of the flaws you pointed out (such as excluding your girlfriend as a witness, because the Court assumes she is just going to say what you tell her to say). If the judge does reconsider and correct the ruling, a new ruling will be issued. If the Judge stands by the original decision, he or she will deny your motion, and you generally have the right to appeal that also.
You must look at your state rules of appellate procedure or contact a local attorney to see how these two suggestions (a direct appeal and the post-judgment motion) affect each other, as you do no want to lose your right to file one by filing the other. This is a very complex and specific area of law, where the advice of an experienced attorney is mandatory.
If the Judge issued a ruling from the bench, listen carefully to his or her reasons. If he or she said you were not entitled to the relief requested, this is generally appealable, as a matter of statutory interpretation.
If the Judge said there was insufficient evidence, ask specifically what was lacking. You can then gather that evidence, in preparation for another request, if it becomes necessary. You can file an alternate pleading, like a Petition To Enforce Visitation if a Petition For Contempt For Visitation Denial is rejected. Family law statutes and caselaw often permit multiple paths to the same goal. Finally, you can simply wait and try again. Your responsibility to raise and visit your children will continue until the family law statutes says they are emancipated, so you will have ample opportunity to request enforcement of the visitation schedule to the court over the next several years. Keep track of your observations and the adherence to the schedule – or lack thereof, and try again whenever your timetable says is best for you and your children.