After upgrading to iOS 8.1.1 my iPhone 5s is saying no service what do I do?

These are some great steps to take.

If you see No Service in the status bar of your iPhone or iPad - Apple Support

Might means that you have unofficially using a different SIM than the one originally for the iPhone.

If you're in your carrier's coverage area

Follow these steps, testing after each.

1. Tap Settings > Enable Airplane Mode, wait five seconds, then turn off airplane mode.
2. Restart your device.
3. Remove the SIM card. If the SIM card is damaged, worn, or bent, or if it's too big or small for the SIM tray, contact your carrier for a new one. Then reinsert the SIM card.
4. Check for a carrier-settings update: Connect to a Wi-Fi network, tap Settings > General > About, and install any available carrier-settings updates. If you can't connect to Wi-Fi, connect your device to a computer that has iTunes.
5. Update your iPhone to the latest version of iOS.
6. Reset network settings by tapping Settings > General > Reset > Reset Network Settings. This will reset all network settings, including Bluetooth pairing records, Wi-Fi passwords, VPN, and APN settings.
7. Contact your carrier to check for any network or account issues.
8. Restore your iPhone.

If you see No Service while roaming or traveling

You might be outside of your carrier's coverage area. If you're traveling internationally, you'll need an international roaming plan to use your iPhone or iPad.