Using Garmin Weather:

If your device supports Garmin weather you just need to connect your watch to a phone via bluetooth and make sure that the Connect App (not Connect IQ) is at least running in the background with permission to your current phones location. (which must be turned on)
The watch will automatically download the weather data from this service which might take a few minutes.

Using OpenWeatherMap:

If your watchface supports OpenWeatherMap as weather data provider and you want to use it, you need a free API key which you can get on their website: https://openweathermap.org/
As soon as you got the key you can enter it in the specific field in your watchface settings. (it might take up to a few hours until a freshly generated key actually works)

Be sure the watch is connected to your phone via bluetooth and the Connect App (not Connect IQ) is at least running in the background to let it download weather data.
If you see a message like "GPS?" on your watch, do a gps fix so that the watchface knows your position. (Get in the starting screen of an activity like "Running" and wait until your watch got a gps signal)

UV-Index / Precipitation on OpenWeatherMap:
If you have an older API key (generated before ~Feb23) you can use this metrics without any problems.
If you generated your API key after that date and want to see these metrics provided by OpenWeatherMap you might need an additional (free) subscription, namely the "One Call by Call" subscription plan.
The first 1000 requests per day based on this subscription are basically free and you can set the limit to 1000 requests which are more than enough to provide weatherdata for the whole day on any of my watchfaces.
If the watchface supports more than one 3rd party weather provider make sure to select OpenWeatherMap as the current weather provider in the dropdown menu in your watchface settings.

Using Visual Crossing:

If you want to use Visual Crossing you need to go on their website and get a free api key. https://www.visualcrossing.com/
As soon as you got your key you can enter it in the specific field in your watchface settings and select Visual Crossing as your weather data provider in the dropdown menu.

Be sure the watch is connected to your phone via bluetooth and the Connect App (not Connect IQ) is at least running in the background to let it download weather data.
If you see a message like "GPS?" on your watch, do a gps fix so that the watchface knows your position. (Get in the starting screen of an activity like "Running" and wait until your watch got a gps signal)