The arms are an important feature of your body - they are the primary tool with which you manipulate the world around you.  When people mention arms in the bodybuilding sense, they are usually referring to the upper arm and, to a lesser extent, the forearms. 

A lot of beginners like to build up their arms because they are the most visible muscle on the body, especially when wearing t-shirts.  They are also the most likely muscle for which you'll receive compliments. 

With that in mind, the arm is somewhat difficult to gain size in due to its constant use and versatility.  By versatility I mean that there are many different muscle groups in the arm that you'll need to isolate effectively if you want to make it as big and as impressive as possible.

Triceps brachii: this muscle is an elbow extensor, which means they it is used for pushing the forearm away from the upper arm. The triceps are the largest muscle in the arm, making up 2/3 of the upper arm. There are three heads on the triceps, although you can generally work all three together. Variations in angles can create additional separation, which'll make you look more ripped.

Biceps brachii: the biceps are the most known muscle in the arm and also the most sought-after. They only take up 1/3 of the upper arm and are an elbow flexor, which means they are used to bring the forearm close to the upper arm. It is important to note, however, that they are utterly useless in this motion if your hands are facing away from your body.

Brachialis: the brachialis is a strong elbow flexor that rests under the biceps. This muscle is highly useful useful since it is not affected by grip and is particularly useful if you're just supporting the weight without actually moving it. If you're holding a dumbbell with your elbow flexed, you'll be using this muscle to support it. This isn't a visually impressive muscle, but it can make your arms appear wider.

Brachioradialis: This is a muscle in the forearm that is also used for flexing the elbow, except it is only useful if you are using a grip in which your hands are facing out or are sideways. Building up this muscle will make your forearm appear wider. It's not the most useful muscle so far as function goes, but it does have its uses - think arm wrestling!

Wrist flexors and extensors: These are two muscle groups in your forearm that are used to move your wrist up and down. They also affect your grip strength. These are good muscles to build up because they'll make your forearm appear both wider and thicker. These, aside from the brachioradialis, are the main muscles in the forearm.

Your grip affects what muscles you target, especially when using the elbow flexion muscles.  There are two types of grip, pronated and supinated.  I'll explain what both of these mean below.

Pronated: A pronated grip is one where your hands are facing away from your body when your elbow is fully flexed.  This means that when your arms create a V, your hands should be facing away from your body.  This grip is primarily used to work the brachioradialis and is not generally useful in real life.

Supinated: A supinated grip is one where your hand is facing your body when your elbow is flexed. This is a more practical grip and is used by the biceps brachii.  You will also be able to move more weight when using this grip, since the biceps are generally stronger than the brachioradialis.

Mid-grip: A mid grip is when your hand is facing to the side instead of away from or toward your body.  This is the grip you'd use when using a hammer.  Because of this, it is one of them more common grips.  This grip will place significant stress on both the biceps brachii and the brachioradialis.

Incline Dumbbell Curl: This is my favorite biceps exercise because it is difficult to cheat with and will offer a greater range of motion than conventional biceps exercises.  This seems to be the best mass-gaining biceps exercise around.  I suggest using an angle of 60-70°.  You can start the motion (elbows extended) with a supinated or mid-grip.  A mid grip will work the supinator forearm muscles and will also offer some resistance for the brachioradialis early in on in the range of motion.

Preacher Curl: The preacher curl forces your elbow to stay still, which allows your brachialis to receive additional strain over your biceps.  A lot of people have a hard time doing this exercise, but you'll probably be able to do more weight with it than the incline curl once you strengthen your brachialis.  This is great for adding mass to your biceps near the elbow, since that's where the brachialis is superficial.

Hammer Curl:  The hammer curl is primarily used to work the brachialis, but it still puts significant stress on your biceps.  They are also great for your forearm supinator muscles, which affect how well you can twist your forearm into a supinated position.  I like combining the hammer curls with the incline dumbbell curl, creating my favorite biceps exercise.

The triceps are the muscle you'll want to work if you want to get big arms.  They take up 2/3 of the total mass of your upper arm and are easier to work out than your biceps.

Lying Triceps Extension: This exercise primarily works the outer heads of the triceps and is a great way to build a horse-shoe shape in the muscle. I prefer to do this exercise with a dumbbell, although it's definitely possible to complete with a barbell. Some people complain of wrist or forearm pain when using a barbell, however.

Close Grip Bench Press: This is one of my favorite exercises that places stress on both the triceps, shoulders, and pectorals. This lift also works the inner pectoral muscle fibers as opposed to the outer ones, which'll help you close the gap between your chest if you have one. If you are just starting out, you'll probably want to do 50-70% of your normal bench press weight, since this exercise is more difficult.

Triceps Dip: Triceps dips differ from normal dips in that you have to keep your hips straight. So long as you do that, you'll place significantly more stress on the triceps than you will the pectorals. Again, be sure to keep your body as straight as possible when performing this exercise.

Cable Push Down: Cable exercises are good because they place continuous resistance on the muscles. Cable push downs will work the outter heads of the triceps and are a great exercise. I like to pair them with triceps dips for the best results possible.

I think the forearms are worked pretty hard in a lot of other exercises, so isolating them isn't one of my biggest concerns, so I apologize if I seem less enthused with this section than the others. I did a lot of forearm exercises with my workout partner because he adored them, but they are probably my least favorite muscles to work.

Standing Barbell Wrist Curl: This is one of my friend's favorite exercises. It is similar to the barbell wrist curl, except you're standing with the barbell behind. Your arms are facing out behind you and you curl the barbell up toward you forearm. You can substitute this exercise for normal wrist curls, but this one offers a greater range of motion. This works the wrist flexors.

Reverse Wrist Curl: This exercise is identical to the wrist curl, except it is performed with a pronated grip instead of a supinated grip. This places stress on your wrist extensors and is a decent exercise.

Reverse Curl: Reverse curls of any sort will place significant stress on your forearms, specifically the brachioradialis. These exercises will also work the brachialis and are great for adding mass to both the upper arm and the forearm.

Getting bigger arms is largely a product of how well you eat and how many calories you consume.  Here are some good diet tips with which you can put on weight:

• Drink plenty of water because it'll help your recovery time and allow you to put on more weight.  Your body uses water to wash away toxins and get nutrients to your cells, so it is imperative that you drink at least a gallon of water a day.
• Your caloric intake is important.  You need to eat more calories than you burn on a daily basis.  This will ensure that you get enough nutrients to your muscles, especially carbohydrates and proteins.  For most people with skinny arms, carbohydrates are the most important because they give you the energy you need to build up the muscle.
• Drink a protein shake after your workout.  You'll want to use whey protein powder so that it is digested as quickly as possible.
  

I just wanted to add a note here that many people seem to see the best results in the biceps when using a high volume routine.  This means you should be doing either a large number of sets, a large number of reps, or both.  When using a high volume routine, however, be careful not to overtrain your biceps and throttle your volume if you're not seeing gains.