When looking to build muscle through working out there are actually a few different ways that you can do this (despite many people think that there's only one way to lift weights and that it doesn't matter how you do it).
Developments made in the last 50 years have shown that resistance training is the best way of building muscle in the shortest possible amount of time.
So what is resistance training? It's essentially working out till you reach the peak of your limits, than going a tiny bit more (which is where the muscle growth happens).
The best way to do it is to use free weights (as opposed to machines) and to do 3 different exercises per muscle group (although you should only work on 2 or 3 muscle groups per workout) and 10-12 repetitions.
The key is to lift a weight that is heavy enough so that you can only do between 10-12 repetitions, and even if you wanted to you couldn't lift anymore (this is called working to fatigue).
After this you should take a 3 minute break (for you to get your strength back) before moving on to the next exercise.
In case you're wondering, the main muscle groups are your chest, arms, shoulders, back, legs and abs.
Also, you should start by working out the largest muscle groups first (such as your chest) and working down to the smaller ones so that you don't tire yourself out prematurely.
Working out like this is (like any form of exercise) will only work if you apply it consistently, but if you do you'll see amazing results!