The steps below apply to the Apple Watch Series 3 and newer models.
Because your Apple Watch uses Bluetooth and Wi-Fi to communicate with your paired iPhone, Wi-Fi is 'always on.' Refer to this wireless connections support page for more info.
Your Apple Watch auto-connects to networks you have joined before that meet the 802.11b/g/n 2.4 GHz standard (i.e., not compatible with 5 GHz networks).
From the watch face screen, swipe up to access the Control Center.
To determine if you are connected to Wi-Fi, look for the indicator in the upper-left of the Control Center screen.
The Wi-Fi icon (upper-left) is displayed in place of the phone icon and the wireless signal icon is highlighted if you are connected to a Wi-Fi network.