Hello Jeff,

first I have to say that I'm not an expert on the Olivetti 36 or any other Olivetti.

What I found on the internet is that the wiring from the On/Off switch goes underneath the machine to the motor as one can see at the end of this video:
Olivetti Lettera 36 Features Review

The wiring is also visible on one of the photos here:
Typewriter Database - 1972 Olivetti Lettera 36 #594248

Electric typewriters are using a rotating drive shaft (power roll) which is driven by the electric motor via a belt. The details could be different for other manufacturers and typewriter models. The rotating drive shaft could either have teeth on it or the surface is coated with rubber like the machine's platen. In the case of the Olivetti 36 it could be a drive shaft with teeth I would assume.
A technical drawing of the Olivetti Praxis 48 that shows that principle:



The toothed drive shaft (1) rotates in direction of the arrow. When the key lever (9) is triggered by the operator the ratchet (2) is tipping over into the teeth of the drive shaft. Over a system of levers the typebar (8) get the necessary momentum to strike the platen.
That's a very short explanation of the mechanics behind a electric typewriter.

Here a Phoenix Typewriter video of a Olympia SGE 35 typewriter with a toothed power roll:
https://www.youtube.com/watch?v=XfJ6nBux8f8

And as an example of a rubber coated power roll here a video that shows it's removal as part of a repair of an IBM Model C typewriter.
https://www.youtube.com/watch?v=Kl-o9bIjw10

This video shows a repair adjustment of individual sticky keys of an IBM Model D. A video that shows also the working of the power roll.
Often a lot of experience and some special tools are needed for servicing a typewriter.
https://www.youtube.com/watch?v=MBK25GOEyck

Have fun exploring and repairing your Olivetti typewriter!
-Rainer

And be careful with electricity - it can bite.
 

My Olivetti Lettera 36 required toothed belts.  But some of these machines, use smooth belts.  The type of pulleys on your machine will determine what style you need.

For my machine...I got 2 sets of toothed v-belts from this on-line outfit : https://vbeltoutlet.com/ The motor side belt was : 145 teeth long, 5 mm wide, and a 2.0 mm tooth pitch. The power-roller side belt was : 153 teeth long, 5 mm wide, and a 2.0 mm tooth pitch. p { line-height: 120%; margin-bottom: 0.1in; background: transparent }a:link { color: #000080; so-language: zxx; text-decoration: underline }

Jeff,

The big black pulley, as you say, is the power roller pulley.  Without a belt, there, your type-slugs will not activate to strike ribbon & paper.

Below is a photo off the Internet showing a machine with flat-belts (and not toothed belts).  This machine in the photo is a later production of the Lettera 36 with its squarish-shaped key-tops, etc. 

My machine is an earlier one when the key-tops were round-shaped.  See 2nd. photo, below.
.
.

Pete E,,

Advice is welcome. I fully understand what you're saying and will look into getting more experience. But I had no idea as to how these things work and am amazed at how simple the concept is. I was expecting a more complicated system that actuated the type bar, not just a continually spinning roller that would propell it.

However, I will be ordering belts so I will have them. That site is a bit difficult to use as it should provide a better search feature, such as entering the details that you provided above. I have to look through their offerings again to find those that you list. I haven't found any 5mm width belts, just 6mm, so I may have to slit them down to 5mm.

Jeff,

Another vendor here in the States to try is McMaster-Carr Co.

On this web page along the left side, they even have a sizing & measuring guide to help you possibly find belts that will work. 
.
https://www.mcmaster.com/products/drive-belts/
.