Summarize:

Modern slings are much more comfortable, ergonomic, and protective than what most individuals can craft. However, arm injuries can happen and you may have to improvise. If you are injured in the wilderness while on a camping trip, if may be impossible to obtain cloth to make the sling above. It is certainly better than no sling at all. Use a sweater, sweatshirt, button-up shirt, or other long-sleeved garment. Tie the garment's sleeves behind your head and carefully insert your injured arm through the loop formed. Allow the clothing material to support the weight of your arm somewhere along the forearm or wrist - wherever is comfortable.  Try to adjust the length of the garment's sleeves that your knot allows to hang so that your arm can hang at a roughly 90 degree angle (horizontal to the ground). If you have safety pins handy, you may want to try "closing" the fabric of the long-sleeved garment around your elbow as a makeshift backstop for your sling as described in the method above. One piece of clothing seemingly tailor-made for improvised slings is the belt, due it having the built-in ability to form a loop with an adjustable size. Secure the belt buckle behind your neck and slip your arm through the loop formed by the rest of the belt. Allow your arm's weight to be supported by the belt along the forearm or wrist. Tie or fasten the belt behind your neck so that your arm is supported at a 90 degree angle. The belt's buckle can be uncomfortable against the back of the neck, so may want to shift the belt so that the buckle is in the length of belt stretching between your arm and neck. You can also put padding between the belt and your neck for greater comfort. If you're injured in an office setting or while wearing formal wear, a necktie can suffice as a makeshift sling until a real one is available. As with the methods above, simply tie the necktie behind in a simple knot your neck and pass your arm through the loop formed. Adjust the positioning and length of your makeshift sling so that your arm hangs at a 90 degree angle. Duct tape can be used very effectively to help immobilize the arm. It has strength, flexibility, and a fabric-like quality which lends itself quite well to this situation.  A loop of duct tape can substitute for a belt or tie, supporting the wrist, arm, and elbow. Duct taping the injured arm to the torso can help reduce movement. Be sure to avoid getting duct tape residue on the skin. Duct tape should be faced so that it does not adhere to the skin. The types of situations in which you'll need to make a sling from your clothing are usually situations in which actual medical care is for some reason unattainable. If your injury is at all serious or persistent, seek the help and advice of a trained medical professional as soon as you can. Improvised slings are usually better than no sling at all, but they are no substitute for a real sling (to say nothing of the other treatments for an injured arm that a hospital can provide). It's better to be safe than sorry - don't risk worsening your arm injury by neglecting to show it to a doctor.
Improvised slings are not as good as professionally-designed slings. Use a long-sleeved garment as a sling. Use a belt as a sling. Use a tie as a sling. Duct tape. Seek medical attention (and/or a real sling) immediately.