Do you have to have "no trespassing" signs up to enforce the law?
From a legal standpoint no. From a practical perspective there needs to be some notification to a person that they can't be there before a cop is going to take action. If a person was on private property w/o permission, with no sign the landowner could in theory never tell the trespasser to get out, call the cops and the cops could arrest the individual. I doubt that would happen very often in practice. And in some cases such as an open lot, the person might be able to argue implied permission. Here the landowner told the person they either pay or get out. Then the cop said pay or get out. And then once they ignored the cop they got a ticket.
Having a sign eliminates the implied permission defense. But so does telling the person to leave. Once they know they are not welcome and remain it is clear cut trespass.