"My approach depends on the individual, but there are a few key things I would do. First, I would bring the situation to light. I would ask the person how they are feeling and if there is anything I can do to support them. Sometimes all someone needs is to be heard and to be allowed to take a brief break to re-energize himself or herself.
If the person is feeling burnt out because they have been working on the same thing for too long, I look for opportunities to shift work around on the team and let them take on a new challenge. Giving someone something fresh to focus on helps in many cases.
If they are burnt out due to stress, I work with them to get to the root of it. Sometimes we need support from additional resources, sometimes the person is not a good fit for the team, sometimes they are ready to move on to another position. Depending on the cause, I work with them to develop a strategy to ensure their needs are supported and the needs of the team are met simultaneously."