This is a question many people get confused on. The prevailing train of thought is, if I want to stay/get thin, cardio is performed first in a workout. If you want to get bigger, lift weights first. Only one of these thoughts is absolutely correct. Can you guess which one? That's right, lift weights to get bigger is the absolutely correct statement. Doing cardio first in your workout can work to get you thinner, but it may not be ideal.
The human body has two sources of energy: carbs and fats. When you perform cardio, the body will use carbs first. Since cardio is slower and steady, it can then use its fat stores as fuel.
Lifting weights is a different story. Because the training is shorter in duration, heavier, more intense; the body can only use carbs for energy. It simply cannot draw energy from fat stores in enough time to supply weight lifting.
Because of this, if a person performs cardio first, it will deplete the body's carb stores. This will lead to decreased performance lifting weights since the body will not be able to fuel itself properly. However, if you lift weights first, you deplete carb stores. This leaves ONLY fat stores for cardio. While you may not be able to last as long, you will burn more fat during your cardio sessions.
One last benefit of weights first. When you perform cardio, you burn more calories than during weight lifting, and your metabolism stays elevated for about 12 hours later. When you lift, although you burn fewer calories, your metabolism is elevated for up to 48 hours. When you combine the two, you will be a calorie burning machine.
So, lets sum this up. Cardio then weights = fewer calories and fat calories burned during and after training. Weights then cardio = more intense weights, more overall and fat calories burned both during and after training. Give it a shot. You should notice significant gains in your weight training, and quicker fat loss.