A proper warm-up is vital before doing any weight training. If time is short, don't be tempted to skip the warm-up and go straight to your workout, because cold muscles can get easily damaged. A few minutes spent on a warm-up can prevent days lost while recovering from injury.
Your warm-up should start with some light cardiovascular exercise, such as running, rowing or cycling. This will make your heart beat faster, pumping oxygen and nutrients to your muscles, and elevate your body's core temperature. Warm muscles are more elastic than cold ones, so you can work them through a wider range of motion with fewer injuries.
After the cardio you then need to target your muscles directly with dynamic stretches. These differ from static stretches in that you are moving as you stretch out the muscle. The trick is to start very gently and then slowly increase the range of motion you use with each repetition. This prepares your muscles and joints for the work to come.
Finally, before you begin any lifting exercise, perform the movements with minimal weight to teach your muscles how to respond when you do the exercise with heavier weights.