Summarize:

In order to receive a software update, your Apple Watch must be at 50 percent charge (or more), and it must be connected to Wi-Fi. Your Apple Watch will update more quickly if it's on the charger than if it isn't. If your iPhone is connected to Wi-Fi, your Apple Watch should be as well. Tap the Watch app icon, which resembles a black-and-white side view of an Apple Watch. You cannot prompt your Apple Watch to update without using your iPhone's Watch app. It's in the bottom-left corner of the screen. This will open your Apple Watch's page. This option is near the middle of the page. It's near the top of the page. Doing so will prompt the Watch app to begin scanning for available updates; if one is available, it will begin downloading. If no update is available, you'll see a message on the page that says your Apple Watch is up-to-date. This can take several minutes. Once the update finishes downloading, you'll see an Install button appear near the bottom of the page. It's near the bottom of your iPhone's screen. This will confirm that you're ready to install the update on your Apple Watch. If this doesn't work, try typing in your Apple Watch's passcode instead. It's in the bottom-right corner of the screen. Doing so will prompt the Apple Watch to begin updating. The update process can take anywhere from a few minutes to over half an hour, so make sure that the Apple Watch stays on its charger until the update is complete. You'll do this on your iPhone's screen. This message signifies that the update is almost complete; once you see your Apple Watch's Watch Face appear, the update has been installed.
Place your Apple Watch on a charger. Open the Watch app on your iPhone. Tap My Watch. Scroll down and tap General. Tap Software Update. Wait for the update to download. Tap Install. Enter your iPhone's passcode when prompted. Tap Agree. Wait for your Apple Watch to update. Tap Dismiss when prompted.