Using an Android Wear device typically requires the watch to be connected to a smartphone through Bluetooth so the smartphone is able to pass data over to the watch, although this isn't a requirement anymore as long as you have a WiFi connection nearby. This is because Android Wear devices can link up to and utilize WiFi networks for a connection now thanks to the added support from Google. The next issue at hand would be to actually complete the necessary steps for connecting to your network of choice, which more or less still requires you to enter a network password on your phone first before the connection manager on Android Wear can do its job.
With an app called WiFi Manager for Android Wear, you can do away with having to pull out your phone and enter the passwords on the larger screen as the app enables the capability to enter network passwords right from the watch itself. More than just being able to enter WiFi passwords without needing your phone, though, the app also allows you to scan for any WiFi networks that are nearby so you can find one to connect to as well which should work great if you're in an area or location that you aren't familiar with and aren't sure if they have WiFi.
You can also use the app to refresh and look for new networks which could come in handy if you're in transit or moving a little a further away from a connection that you found initially. Of course, a WiFi manager wouldn't be complete without details of the network you're connected to or the networks that are within range. The app does have a details feature, simply tap on any network listed and it will bring up the details of the network like link speed, signal strength, channel, security, IP address, and more. You can also sign into public networks that require a guest sign-in process, like at Starbucks for example, which will require you to accept the terms and conditions before supplying you with access to the network. The app is free to install and try out, and it should support all Android Wear watches except for the original LG G Watch and the ASUS ZenWatch.