If you are replacing existing equipment with something new, and not moving to a new location, its pretty easy.
I have changed weather station hardware at Weather Underground and kept the same Station ID. Just turn off the old station sending data and turn on the new station sending data. Use the same ID, and you will need to know your WU "key", which can be found in your WU account, Member settings, then "My devices". Put the Station ID and the Key into the new hardware setup.