A manager has to take any such accusation seriously. However any well-run business will have a process for handling these types of claims. As a manager, he should first go to HR and ask for direction on how harrassment claims should be handled. The main thing is that he needs to make sure the process is followed to ensure the company does not get into legal trouble for how it treats either party in this.
In general the first step is usually to have the person directly tell the other person to stop harassing her. If that doesn't work, then you need to have the person follow up in writing. She should come to the manager with a list of dates and times and an account of the incidents. She should be able to tell him exactly when she told the other person to stop it. It is important to document what is happening even if no one can see it.
In the meantime the manager should be looking out for how these two interact and see if he can see evidence. In particular, if the woman gets up and then the man gets up and follows her, the manager may want to do so as well. If he hears any sexual innuendo from this person anywhere in the office whether the woman is present or not, he should be told in no uncertain terms that such things are not appropriate in the workplace. Of course, if you tell him that he can't make those kinds of comments, you have to make sure you don't let others say such things without a similar warning. The manager might also consider sexual harrassment training for all of the team, so that it is clear what is and is not harrassment and what actions can be taken if someone complains.
You may also want to make sure these two people are not assigned to work together if at all possible until this is resolved.
Since this kind of behavior can escalate to actual rape very quickly, the woman may want to make sure she does not go places like the parking lot alone especially if she works late at night.
If the person persists after being directly told to stop, then the manager can step in after ensuring the woman does in fact want to make a formal complaint and is aware that the person will be told details of what he is accused of doing and that while you will maintain confidentiality, the person who is accused may not. Then he would call a meeting with the accuseed, usually with an HR person in attendance, and tell the person what he is accused of and ask for his side of the story. Then after hearing his side of the story, the manager can decide what actions to take. It coudl range from no action, to an inofrmal warning to avoid being alone with this person to a warning in his personnnel file to a suspention to being fired depending on what the details are and how much of a threat he seems to be. Any actions taken shoud be only after consulting with HR (Or a lawyer represnting the company of you have no HR).
If you have no HR, the manager needs to go to the CEO of the company and tell him there is a problem and ask that a lawyer be consulted. This is to protect the company from being sued.