I'll show you how to update your firmware using the Basecamp software. This is a free program from Garmin.
When you plug in your GPS device, like a MAP 62, you might get a notification alert on the top right of the screen. By clicking on it, you may opt to apply the update or not.
From here, the Garmin webupdater software takes over and downloads the firmware, then transfers it to the device. Other devices might reboot automatically, but for MAP 62 needs a manual restart.
Once it restarts, it will validate the firmware and apply the update via the software loader. You will see a progress bar.
Once done, a final reboot is done and you should eventually see the last screen you were at.