Hi,
The experts on here recommend that people read the IH owner's manual for the model and approximate year of their tractor.
They don't seem to have an A owner's manual on here, in the manuals I looked at. There may be one at Resources, but you can't get to those when you are new on here.
The IH owner's manuals for other tractors that they have on here have lots of info about operation, maintenance, and lubrication.
You can probably buy a paper A owner's manual online somewhere. Binder Books is probably a good place to buy one, they have or used to have IH manuals.
The engine may need a tune up, the points might be burned, or corroded from sitting, that can make it start harder than it should, and run rough, or not run. The points need the right gap also.
The engine might have a valve stuck open from sitting.
The ignition timing may need checking and setting.
I would check or change all the oils before using the A, using it with low oil in a gear housing can damage the parts in the housing.
There are 3 separate gear housings, with 3 separate oil levels to check, in the rear area of an A, the transmission, and 2 final drives.
The air cleaner is an oil bath air cleaner. Dirt that is sucked in settles to the bottom of the oil cup. It should have clean, light motor oil in the oil cup to work right.
I would oil the fan hub, something often not checked, people on here have said.
They can get low if nobody checks them, then the fan bearing can wear, or the fan can seize up.
The owner's manual may tell how to oil it, I don't have an A owner's manual to look at.
Something sometimes not greased as often as it should be is the clutch throwout bearing.
There is a search box at the top of the page, to the right of the Farmall Cub, you can find info in posts that have been made.
There is an A and B parts manual on here, here it is below. It doesn't tell much of the info that the owner's manual does. The B is another model of IH tractor, parts for those are in this manual too.