One of my Surivors got injured. What can I do?

As long as your Main Building still stands, you can keep playing. If a survivor gets injured on a mission or during the night, you have to wait until he has fully recovered. This will take several days.

If you need him to be back on his feet earlier, you can build the Sickbay building. It serves as a hospital and injured survivors will heal faster.
Upgrade it to speed up the recovery even more.