The Importance Of Warming Up
The obvious reason to warming up is to prevent injuries - and although staying injury free is THE most important aspect to training, this doesn't seam to be a big enough reason for people to warm up. So I am going to try and sell it to you in another way:
Get everything firing to lift heavier
By warming up you are preparing your central nervous system, muscles and joints for battle with the iron. A proper warm up will get these warmed and lubricated up ready to move some serious weight...
Think of it this way... A warm up will prepare your body the same as starting up a ferrari. First you fire the ignition, secondly you put it in 1st gear and pull off. Once you have peaked 1st gear you go into 2nd, 3rd, 4th and 5th. Once you are in 4th you have all the power of the giant engine at the end of your foot with 1 simple push of the accelerator.
By warming your body up you are essentially putting it into 5th gear - prepping it so you are ready to fire that accelerator for your bench, squat, dead lift or any other motion.
Full body warm-up
It is all too common to see people only warm up their legs on squat day, or only warm up the arms and chest for chest day. Working out in the gym requires your entire body to be active, you may not realise it but with the majority of lifts, even isolation lifts your whole body is under tension in some way or another.
Don't waste your warm-up. Take advantage of your warm up and use it to concentrate and focus on your workout. Go over in your mind how you can improve each lift. Think about the range of motion, how you can contract harder, how you can recruit extra muscle fibres or focus on a certain aspect of the lift. Think about what weights you want to lift and for how many reps. Use the warm up to mentally fire yourself up, prepare yourself for the mind-body connection and to push yourself harder than ever.
Focus on lagging or tight areas
Use the warm-up to focus on body parts that are lagging, tight or weak. If you have tight hamstring and calves, include some extra work to stretch and get these firing. If you sit down all day at a computer - you might want to incorporate some hip or posterior chain movements - working on your weak areas for just 5 minutes 6 days a week will bring them up in no time, you will most likely also turn these into your strong areas.
Here is a great video from Mens Fitness showing you an example full body workout.