How do I gain muscle? I'm skinny want to get bigger arms I work out at least once a week but just get cut how do I get bigger?

More calories. You are most likely a young, active male. If you are, then most likely you are burning more calories daily than you are taking in with your diet. In order to bulk up, increase your calories, adding both fat and carbohydrates. Next you shoud decrease some of your cardiovascular work. If this fails, get a dietitian to evaluate your diet in detail. Good luck.
Agree w info you. Have already received. Going for big guns. These exercises help to build arm muscle: push downs, pin presses, dumbbell wrist curls, dips, rolling extensions, barbell wrist curls, preacher curls, chin ups, lying barbell triceps extensions, thick grip curls, concentration curls & lying dumbbell triceps extensions.
Big muscles. High repitition lifting is good for toning and caloric burn. However, to build muscle you need to work with sets: 7 reps max; 5 reps max; 3reps max efforts. Work alternate muscle groups one day later. And a five time per week effort is needed. Free weights are better than machines, because they use the small stabilizing muscles of the joints being exercised. Finally, 2g of protein per pound!
Excercise and diet. There key factor is strength training is resistance exercise. This means weight lifting or calisthenics ( where you use body weight for the resistance). Once a week is not enough to have a meaningful effect. A regimen of 3 time/week is best . Use a workout that conditions all muscle group. A diet with enough calories and especially protein may help. Advice from a coach or phys ED teacher may help.