There are really only two basic motions you can do to build your arms: bicep curl and tricep extension. Naturally, there are hundreds of variations of these motions that you can choose from.
To tone my biceps, I like to curl dumbbells. Choose a weight you can curl ten times. From here you can curl in the traditional fashion and work the biceps. Then, switch to a hammer curl. This is where the dumbbell is facing North and South and looks like you are holding a sledge hammer. This variation works your forearms and biceps and you may be able to up the weight with set. Then lastly there is the reverse curl. This variation has your palm facing the ground and you bring the back of your hand to your shoulder. It is much harder than the first two versions and works your grip really well.
To build muscle mass, I love to use a bench bar. Use the 45 pound bar, or whatever weight you can curl, six times. Doing this variation, I only do the traditional motion. When I try to do reverse curl, it torques my wrists.
The key with all of these variations is not the motion or even the weight, it is the technique. It is important to take your time and control the weight. I like to do a two count to the up position and then a three count down. On my last rep, I do a negative rep where I hold the weight at the point I feel the burn the most and see how long I can keep it in the up position.
Personally, I do not like to do biceps and triceps on the same day. My routine is usually simple. I do three sets of traditional dumbbell curls. Then I do my heavy bar for five sets. After that, I do three sets of hammer curls and two sets of reverse grips. After this my arms are usually marshmallows and I am ready to move on to something else.
Triceps are worked a lot during benching and push ups, so I try to do exercises that vary from that motion. I have spent whole workouts just doing dips and have been satisfied. However, I have had great success just adding dips into my chest day and not dedicating too much time to triceps alone. I think this works for me because I do push ups often and am constantly working them.
To do an overall arm workout if you choose, do the above bicep workout and add a set of 10-15 dips between each set of hammer and reverse curls. This will provide you with some sculpted arms by midsummer.