Large Muscles First

Exercise the large muscles-groups first before starting on the smaller ones. This means that the large muscle-groups of the chest, legs and back should be exercised before going on to the arms and shoulders.
Exercising of the larger muscle-groups both mentally and physically taxes your system quite heavily. With these larger muscle-groups many other muscles are involved to help finish the exercise.
Take bench-pressing exercises, for example, for training the chest. To do these exercises you do not only use your chest muscles. Your back and triceps also have to work quite hard to lift the weight. Before doing the bench-pressing exercises you could first exercise some smaller muscles like the triceps and biceps.

Take heed, however: there is a good chance that these strenuous bench-pressing exercises will tire the triceps before tiring the chest muscles. If that should be the case, you will not have trained your chest muscles sufficiently that day for growth to take place.
Moreover, you will probably have strained the triceps, which may even slow down growth!
Therefore, when starting up your workout, do the exercises involving multiple muscle-groups (compound exercises) first.