"Unfortunately a kiss on your boo-boo wont solve things in UOPhoenix"
The healing skill will determine how likely you are to succeed applying your bandage in the midst of battle. Having a high Dexterity score will help immensely, reducing the amount of healing potential lost when you slip your fingers and reducing the overall time it takes to apply a bandage.
A skill any warrior should have, but isnt rare on Mages either. The best option is to go around the farmlands collecting cotton and shearing sheeps, and spend some time working in Tailoring shops. Cut up the cloth a few times to end up with clean bandages. Optionally you could directly buy Cloth or Bandages from the vendors, but this could be expensive for newer players.
0 - 30 Go to any house of healing, and spend a few gold coins to get started.
30 - 60 Hunt monsters and get hurt, heal yourself by using a bandage on yourself. Or find a friend to hurt you or hurt him, whenever blood is spilled you can train your skills. Note that healing others is faster then healing yourself.
60 - 80 Continue healing as you did, if you have anatomy at 60 you can now also cure your poisons.
80 - 120 Still healing yourself? Good. But you might consider at this point to kill a friend and try resurrect him if your anatomy is above 80. Tell your friend to stay dead. *evil grin*