You need to have Network or Multi-User option for your software to do this
  1. Open database as Admin user
  2. Next go to File
  3. Network Administration
  4. For users you want to add password for enter password in Password box
  5. Then re-enter in Confirm Password box
  6. When Finished click Done
  7. Now when selecting that login on this database users will need to enter appropriate password
User-added image