In addition to iOS 10, Apple on Tuesday also released watchOS 3 for the Apple Watch. The update, which has been in beta for the past 3 months, is free and compatible with all available models of the Apple Watch.
To install the new software, you'll have to ensure your iPhone is on iOS 10. Once that's confirmed, simply open the Watch app and navigate to General > Software Update. Your Watch must be within range of your iPhone on Wi-Fi, connected to its charger, and have at least 50% battery life.