Google added support for WiFi on Android Wear devices a long time ago, but the feature is a bit of a pain to use. You have to enter the WiFi passwords on your phone, and the connection manager on Wear is limited to say the least. WiFi Manager for Android Wear makes more of the process workable on the wearable itself, and it's free to try.

WiFi Manager for Android Wear comes from Appfour, which has made a number of bizarre Wear apps that have no business existing (eg. a Wear web browser) and some that are rather useful (Photo Gallery for Wear). This app falls into the second category, I think. Open the app on your watch and you can scan for nearby networks, enter passwords by voice or with a built-in keyboard, and manage your connections.

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The phone app has some additional settings, but not all of them are available for free. If you want to input static IP addresses, use a smaller keyboard, or connect to open networks from the watch, you'll need the $2.99 full version.