Let's look at the simpler situation first. This is burnout not caused by stress or frustration, but rather by working too hard and too many hours by choice. This situation sometimes fixes itself. You work too hard and then start burning out, so you slow down. If you find yourself unable to slow down, you have to force the matter. Find out how much vacation time you can take and then take it. Make a point of leaving work on time. Don't take work home with you. Start slowly if you have to. Leave work on time one day a week and then increase it to two days. Make sure you spend the night relaxing — rent a movie, or read a good book.
It's a whole different matter when your burnout is caused by stress or frustration. Usually it's an outside force causing you to feel this way, i.e. a difficult boss, more work than you can handle, or impending layoffs. A difficult boss is a tough one because if you work for someone who is just not a nice person, there's not much you can do to change that. However, you may consider sitting down with him or her to discuss how you can forge a more productive working relationship.
If you have more work than you can handle because of a smaller staff, you have to learn how to better manage your time. One person cannot do the work of five people regardless of how good he or she is and how hard he or she tries. You'll have to figure out what is most important and work your way down from there. It's imperative that you stay organized so things don't get lost in the shuffle. You should also stay calm and remember that the world won't end if you don't get everything done.