Install Serum from the Splice desktop client (Windows users need to take note of the installation destination, by default under the User’s Documents folder).
To get Serum up and running in Ableton you need to check Ableton's AU/VST settings.
Navigate to :
File and Folder(all Live versions until 10.1)/Plug-ins (Live 10.1 and later)
Make sure "Use AudioUnits/VST" are all checked and hit Rescan.
Windows users will only have the option "VST Plugin Custom Folder", manually navigate to the location you installed Serum.
On a Windows machine, when you install Serum it asks for a VST 64-bit destination. This installs a Serum_x64.dll file into that selected folder which is a VST2 plugin.
In Live 10->Preferences->Plugins set the VST2 Custom Folder to ON and you want to set that VST2 Custom folder to the location containing Serum_x64.dll
VST2 plugins don't have a default installation location. Common locations users choose for VST2 installation:
C:\Program Files\Common Files\VST2
C:\Program Files\Common Files\Steinberg\VST2