A few ways to do this on many of the Garmin models (maybe not yours, in which case you should check your manual)
From the watch - Menu > Connectivity > Wi-Fi > My Networks > Add Network > Select your new Wi-Fi network. You can then enter the password on your watch. Alternatively, a keyboard will open on the Garmin Connect app on your phone where you can enter the password.
Using the Garmin Connect app - More > Garmin Devices > select your watch > Connectivity > Wi-Fi > My Networks > Add a Network
Using Garmin Express with your watch connected to your computer.
