If an update is available, it will be downloaded automatically usually.
If that is the case, wait until the update has been downloaded, and click on the relaunch button to complete the installation of the Chrome update. Maybe because something is blocking the connection to the Google servers to check for Google Chrome updates, or maybe because of corrupt files.
The standalone installer comes with everything included to update Chrome, the Web installer will download data from the Internet during installation.
Simply run the installer on your system and wait for it to complete.
Select Edit, upload the new package, and hit Publish.