The type of bandage you have dictates the type of use. Ideally, you d use sterile bandages where the area needs to be kept as clean as possible. Styptic powder is an effective coagulant for minor wounds. That is, it stops bleeding from things like small scratches, a nail trimmed too short, etc. A major brand is Kwik-Stop, which you can get at a pet store or from a vet supply company.
Any brand is fine, and there are different forms.
You can get it in a plastic cup with a flip top, a pencil , pre-dusted pads, etc. The idea is to get a liberal amount of the powder onto what is bleeding. You can scoop some with a finger and touch it to the wound. With the pencil form, you can stick the nail directly in the tube, although you d have to sprinkle it out for a wound not on a toe. You can either wash the styptic powder off with water, or use Betadine to rinse it.