Building muscle is one of many possible goals to have when it comes to physical exercise. Other goals include strength training, endurance training, and balance/coordination training. Focusing on building muscle (at the expense of other goals) is not necessarily healthy.
Building muscle mass to the level of the serious bodybuilders we see on the covers of glossy "health" magazines requires that a person lift very high weights (and use low reps, sometimes just 1-3 reps), and thus it can easily lead to injuries, particularly of the shoulders and knees. I avoid very heavy weights, and I prefer free weights over most machines (with the exception of cable machines, which can be amazingly effective) and try to focus on strength, endurance, and form/coordination when I'm using weights. I also like variety, as the same thing over and over tends to bore me pretty quickly.
Thanatassa's initial post is very good, but it focuses on a balanced program for strength training, not a focused program for muscle building. In addition to what has been posted here, I would add that a person wanting to build muscle needs to eat frequently (eat well and eat often) and needs to get a large amount of sleep.
The best way to build muscle if you are new to weightlifting is to use strength training machines at a gym. Choose weights you can lift no more than 12 times and do 1-3 sets of 8-12 reps. Make sure to work all major muscle groups using both pushing and pulling motions. A typical balanced workout should include chest press, seated row, lat pull down, overhead press, flyes, leg press, stability ball abs, leg extension and leg curls. Add preacher curls and triceps extensions if you have extra time. Alternate days doing strength training and cardio. For food, eat a health balanced diet, making sure to include 1.2 to 1.5 grams of protein per kg. of body weight. Don't take supplements -- most of them are useless and some are harmful.
Check out reputable sites like the US Food and Drug Administration and MayoClinic.com for accurate information about supplements.Trusting a site that is pushing supplements, and depends for its income on selling them, for impartial information is not a good idea. Really specific bulking and cutting diets are only relevant once you've been lifting for at least a year at a very high level.
The above answer is just about perfect except the supplement argument. If you should avoid anything, it is steroids, not supplements. fake supplements can cause a health hazard. So, don't take a supplement till you are sure that it is an authentic one.
The fact about supplements is that they are used effectively by almost all sports-persons in competitive sports. Supplements have been invented for the sole reason that you cannot carry truckloads of food where ever you go (believe me, once you start bodybuilding you will consume an unbelievable quantity of food, especially if you are thin). So, don't be scared of supplements and just remember that the best bodybuilder is also the most knowledgeable one. So, read everything you can about this wonderful sport.