Skip to Step 3 if you already have VCMI installed.
Open your web browser. Go to the GOG website and download the offline installer for Heroes III. Create a new folder somewhere accessible to you (like D:/Games/Heroes III VCMI) and install the game there.
Install the latest version of VCMI to this same folder. Do not install it to any new folder it tries to create - it must be installed to the game folder (D:/Games/Heroes III VCMI).
Launch VCMI_launcher.exe and install Tears of Ashan.
Disable Horn of the Abyss > Main menu theme submod if it is still enabled. OPTIONAL: Disable Horn of the Abyss > Cove > Cove Music Theme by Heroes Orchestra submod.
Launch the game!
Delete the old version of the mod.
Drag and drop the new version of the mod into C:\Users\USERNAME\Documents\My Games\vcmi\Mods.
Navigate to C:\Users\USERNAME\Documents\My Games\vcmi and delete any \maps and \saves in their respective folders using the previous version of the mod. This step is necessary to prevent crashes or errors with old saves as the mod evolves!