Depending upon how much latitude a supervisor may have, the supervisor can motivate in a variety of ways. The first step is to find out more about the situation, so that the best motivation strategies can be used.
The supervisor needs to sit down with the employee to find out whether this attitude stems from family problems that the worker is more focused on or because of a feeling of disengagement in the workplace. We also need to know if this is a situation in which the employee's performance is actually deficient or if the employee is, in fact, doing the job and perhaps not exceeding expectations. Motivational strategies are going to be different, to deal with very different sets of facts.
If an employee is not focused as well as he or she should be because of problems at home, there are several means of helping and motivating the employee. The most obvious is to offer the employee the resources available through an employee assistance program (EAP). These programs offer counseling or therapy, along with guiding the employee to community resources that can help with the problem. In a situation like this, working toward a solution at home may very well help the employee to be more productive. Another means of helping and motivating the employee, if this is possible, is to offer some sort of flextime or job-sharing that would allow the employee to meet the obligations of home, thus freeing the mind for better performance in the workplace.
If the employee is simply disengaged in the workplace, other strategies will be more helpful. One is to cross-train an employee, providing new challenges that will stimulate him or her. Another is to expand the employee's area of responsibility. He or she may simply be bored. Still another way is to make the employee responsible for training someone else. This places the employee in the position of being a role model and encourages the employee to show competency or proficiency, which is a great means of enhancing performance. An employee who is so disengaged there is no interest in promotion is likely to benefit from these strategies, too. Rewards are always an option, as well, for the supervisor who has the authority to use them, for example, bonuses or some friendly competition for "Employee of the Month" awards. But as a general rule, I would say providing internal rewards, satisfaction in a job well done, is a better means of creating enhanced performance than external rewards such as these.
If an employee's performance is actually deficient, more negative kinds of motivation might be necessary if none of the above is helpful. First would come notice to the employee, along with some counseling. But if this does not elicit improvement, often some form of discipline might be necessary, a disciplinary memo, then a suspension, without pay, all of which could very well lead to termination. Negative reinforcement is seldom the best way to begin motivating people, but at some point, if positive reinforcement is not working, a supervisor cannot disregard poor performance because there comes a perception of unfairness on the part of other workers, who are doing their job and often will resent carrying someone who is not.
So, the first step is always to ask why this problem exists. Then, with that information, there are many tools with which to motivate the employee. I think it is always best to begin with positive reinforcement, which is far more effective than negative reinforcement.