When I first began lifting weights I would typically work biceps with back and triceps with chest. As I spent more time weight training and learning about my body, I found that I could get more growth out of my arms by dedicating a day solely to them. On occasion I do still use a traditional chest/triceps or back/biceps split, because I believe that you need to constantly challenge your muscles with different methods in order to continue to see improvement. However, when I am able to stick to my normal gym schedule, I prefer to give them their own day.
I tend to start and end with cable movements, because I feel like they are a great way to warm up and also exhaust the arms. Here is a typical arm workout that I would perform.
1a) Reverse Grip Cable Pressdown, 4 sets of 15-20: I use an underhand grip with an EZ curl bar attachment at a high pulley cable station. Facing the station, I straighten my arms to flex and then return my arms to a bent position, while keeping my elbows to my side.
1b) Low Cable Curl, 4 sets of 15-20: Remaining at the cable station, I lower the EZ bar to the bottom and use it for curls. I find this superset is a great way to get my arms warmed up before moving on to free weight/bodyweight exercises.
2a) Standing Barbell Curl, 3 sets of 8-12: I tend to use a shoulder width underhand grip for most training days. Keeping my elbows pinned to my sides, I curl my arms to the top, hold for a count and then slowly return to the starting position in front of my thighs.
2b) Standing Dumbbell Overhead Extension, 3 sets of 8-12: Holding the inner plate of a dumbbell with both hands, I lower the dumbbell behind my head bending only at the elbows. Once I hit a full stretch (around 90 degrees), I return to the top of the movement.
3a) Seated Hammer Curls, 3 sets of 10: I like to do these seated on a bench (they can also be done while standing), using dumbbells with your palms facing in (neutral position). Curl the weight to your shoulders while keeping your hands neutral.
3b) Skull Crushers, 3 sets of 10: Performed by lying face up on a bench while holding an EZ curl bar directly above you. Bend your arms at the elbow toward your forehead, once you are slightly past 90 degrees, return to the starting position. I like to finish up each set with a set of 10 close grip bench presses using the same weight.
4) High Pulley Cable Curl, 3 sets of 15: Standing in the center of a pulley station with both sides at the highest position. Using D handle attachments, start with your arms stretched out in a cross and slowly curl the cables toward the sides of your head, squeezing at the peak position. Return to the cross and repeat.
5) Cable Kickback, 3 sets of 15: Done at a pulley station with the cable set at the lowest position. I prefer to do this without any attachment, using the rubber ball as the handle. Bend at the waist until your upper body is parallel to the floor. I keep my upper arm in line with my torso and extend at the elbow flexing my triceps at full extension, before returning to the bent elbow starting position.
6) Dips, 3 sets to failure: At a dip station, slowly lower yourself between the parallel bars by bending your arms at the elbow. Again, after going below 90 degrees return your arms to a full extension. I usually do body weight dips but sometimes I substitute in machine dips as a finisher.