I'm about to remove my engine from my W123 300D to get the lower oil pan straight and to see what on earth is causing those great plumes of smoke.
In principle it seems like a straightforward operation. You need an engine crane and a balancing attachment (sorry don't know the name for that bit). This is clearly shown in the picture in post number one of the thread link below.
It seems best to take out the engine and the gearbox together. FSM and Haynes say so.
You disconnect everything between the engine and the chassis and pull it out!
In your situation I'd be more worried about making sure that your replacement engine is worth the work. Have you done a pressure leak test or a compression test?
This is the thread - but it doesn't give much info on getting the thing out...
Konstan's 1982 300D Engine Out Thread