What do I need to do and know to replace a part in the toilet tank?

I’m house sitting there was a loo with a slow flush. Well this morning it wouldn’t flush at all. I opened the tank tugged on the plunger lever which happened to be extremely brittle. It snapped.

So I need to know if there is any specific information like the model number or measurements for a replacement part. Also any tools I might need and tips from the professionals about the installation process.