What are some things that I can do when my toenail has separated?

Bandaid. Place a bandaid on it to prevent the remaining part from tearing off. See a podiatrist.
Bandaid over nail. Usually when a nail seperates from the nail bed it is caused by trauma or fungus. You want to try and not rip off the toenail accidently. You may want to see a podiarist to get it treated.