Do this step by step for the weather “APPLET” (weather “EXTENSION” is done differently):
Download the weather applet from "here"
to your downloads folder.
Open your downloads folder.
Unzip (extract) the downloaded file to the desktop.
Goto your desktop.
Open the “cinnamon-weather” folder you just created.
Run “cleanup.sh” in a terminal entering root password as required (clears any previous installs)
Run “install.sh” in a terminal entering root password as required (This does more than just copy the files into /applets (read the “install.sh” code)).
Press alt/F2, type r, press enter to restart cinnamon (instead of logging out and back in).
Open cinnamon settings-->applets and activate “cinnamon weather” by clicking its check-box.
The weather applet should now be in the panel (If not, restart cinnamon as above).
Click the weather applet in the panel and then click the gears in the upper right corner of the applet popup box (opens a popup window).
Enter your WOEID (or zip code if US) and press enter. Set other parameters as needed.
Close the popup window.
Drag n' drop the applet to where you want it placed. If placed in bottom panel then press alt/F2, type r, press enter to restart cinnamon or the popup will open in the wrong direction.
When all is working you can go ahead and delete the “cinnamon-weather” folder from your desktop and the downloaded file from your downloads folder.
That should be all that needs to be done.