I am so glad you asked this question; as a hand surgeon, I often see patients in the emergency room after unfortunate accidents involving their fingers. Most people bring the part in "on ice." Unfortunately, putting it directly on ice can damage the tissue. The best way to preserve the part is to wrap it in gauze moistened with saline (salt water), place the wrapped part in a plastic sealable bag, and put the bag on ice. This helps to preserve the tissue in case the surgeon is able to reattach (or "replant") the part. This is a great technique to remember; hopefully, you never will have to use it!