Log into the battlenet (blizzard) application. Select StarCraft II and hit repair. This part does not require any active StarCraft II licence. Warning, this might involve moving some large amount of data depending on if the game is patched or if any files need repair.
Using the StarCraft II editor requires an active StarCraft II licence. Make sure one is attached to your BattleNet (Blizzard) account. In theory only 1 of the core game liscences (WoL, HotS or LotV) is needed to use the editor but I am not sure. The licence key should come with any physical disc version of the game.
Start the editor. I recommend from the BattleNet (Blizzard) application as that should hopefully auto authenticate you. Otherwise login to your BattleNet (Blizzard) account when prompted inside the editor. If the locale is wrong go to preferences and select your desired locale. This can be tricky for obvious reasons but preferences is somewhere under file which is always the far left pulldown menu. An editor restart may be required. It may also be required that you start StarCraft II and select your locale there. Do be warned that changing locales may require the game to go and download the new locale files which can be some large amount of data. Finally start the editor after all/any downloading is complete and it should work.