When you install Addons, you first want to make sure that RoM is closed. Then download your addons to the proper folder, and simply launch the launcher again. Couldn't be easier. If you are having issues with it downloading this or that, or your launcher fails to start, then visit the RoM forum, and search for 'manual updates'. Simply download the latest update that your system has, and put that in the RoM main folder. Then launch the installer. It will launch, install the update, and the game will work again. Make sure you check your ini (configuration file) as well to make sure it's pointing to the proper servers! other than that, there are not many issues w/ it.
Might i recommend, however, that if you like to use addons for RoM, install the Curse client. It's a great program that supports RoM without issue. It manages all addons, updates them, installs them, and launches the game for you. No need for you to extract, move, copy, blah, blah, it does that for you!