The required knowledge to put this nice lathe together is not learned by reading a few comments on your request. You need to get familiar with lathe work. YouTube can help and that takes time but it is well spend. Maybe a forum member in your neighborhood can help you get started.

Lathes UK will provide more information.
the wooden piece with hinges looks to be the countershaft.

The motor having been made in Toronto, and a little battered, may very well be old.

If this is your first lathe, do buy some books, and study them, Only when you have a better idea of whats what try running the lathe. Then try cutting metal.

Stan Bray “Basic Lathework”, or Harold Hall ” Lathework – A Complete Course” would be good for starters.

Remember that the cut that you put on will come off both sides, so a 0.005″ cut will reduce the diameter by 0.010″.

The tool needs to sharp, and with the cutting edge set at centre height.  If it isn’t it will not cut properly, if at all!

It is only a small lathe so don’t go looking to churn off 1/4″ a side.

In the right hands, it can do good work, within its limitations.

You will need some measuring equipment, such as a calliper, (Vernier, Dial or Digital; your choice).

If you PM me with an E mail address, I can send you a copy of “Notes for Newbies” which you might find useful.

Howard

Can you set out the loose parts and photograph them? That will help anyone here help you identify them.

Fior exanple: the small rectangular block on the ground between the lathe and red box in the first photo, seems to be the top-slide so you need know how complete that is. It should contain a screw with a bearing and handwheel and those might be loose in the box.

Those gears with the key-ways are likely the “Change-wheels” used in various combinations for cutting screw-threads. The numbers stamped on them are of their teeth-counts, used in working out which wheels for what threads.

You’ve a goodly collection of tools there, probably all High-Speed Steel, so you’ll need a bench grinder for resharpening them, with introductory books on turning explaining their shapes.

Though those things in the wooden box look like grease-guns, lathes like this are normally lubricated with a light oil.

A tip on what steel to learn on: use a “free-cutting” grade. Many grades of steel can be right so-and-sos to turn satisfactorily so until you’ve enough experience to handle those, use metals that should return good results reasonably easily. If you use steel from an unknown source – as I am wont to do – you might be lucky but are very likely to find it is something very tough, tears rather than slices, and generally gives you grief. (Free-cutting steel, typically containing a tiny trace of lead, was developed for high production rates in industry.)

First things first though, give the lathe a good cleaning and oiling, set it up on a suitable bench, sort out what are lathe parts and accessories and what aren’t in those boxes.