First aid for someone who got their arm cut?

Laceration. The most important points to make is to control bleeding with some type of pressure and keep the wound clean. If you have tap water available then make sure the cut is clean before applying a dressing. If not then keep it covered until you are able to clean the cut.
Arm cut. Clean with an antiseptic and apply a sterile bandage.

Related Questions

First aid use triangular bandage mike elevation sling came underneath arm and bihind back if I tie on shoulder don't go behind back will hurt person?

Not sized correctly. The triangular bandage is sized incorrectly. I suspect it is too small for the individual if it does not swing around the back. You can let the arm "dangle" from the neck (i.e., one strap goes over each shoulder & tied behind the head) temporarily. But as soon as possible, get a properly sized sling & support the arm correctly. After all, this is "first aid": use in emergencies until help arrives. Read more...