In most cases, your Chromebook will stay up-to-date automatically.
However, if you'd like to manually check to make sure your Chromebook is up to date, you can do the following:

  1. Connect your Chromebook to the internet.
  2. Click on the settings tray in the bottom-right corner of the screen.
  3. Enter the settings using the gear icon.
  4. Click on “About Chrome OS” on the bottom of the left column.
  5. Select the “Check for updates” option.
  6. Once the update finishes downloading, click “Restart.”