The question that follows is, "what sort of oil do I use?". The answer is both simple and tricky. The original service manuals call for SAE 20 oil-- this is your basic petroleum-based oil of light weight. It is pure and does not contain detergents or vegetable derivatives. Sturmey Archer actually made and marketed their own oil, for the purist.
You should not use heavier substances like heavy gear oil, 50 weight motor oil, etc. You also should not use substances like WD40. WD40 is great for cleaning hubs filled with junk, but not for lubricating a ready hub. The one place you can use a little grease is on the hub bearings, assuming you want to take the hub apart (most avoid it).
So you can use SAE 20 motor oil from the auto parts store. I use SAE 20 because I tend to like sticking to the original spec stuff. However, I buy it in small, blue and white cans made by 3 in 1. It is called 3 in 1 "motor" or "electric motor" oil.
One substance that is advertised specifically for bicycles is 3 in 1 Standard Household oil. It comes in a black, red, and white can. The label is black, not blue. This oil tends to congeal in hubs and leave a nasty, sticky mess. If you want to use a 3 in 1 product, use the blue label "motor" oil shown above. I've heard of people using automatic transmission fluid and Phil Wood products as well, but have been perfectly content with SAE 20, so why mess with an original, working formula?
Today, most internal gear hubs rely on grease and do not involve oil filler caps. These hubs can be given a shot of life now and then by slipping some oil in the hollow side of the axle, but a full re-build means taking it apart and re-greasing. I tend to prefer the old ones, which require periodic oiling but rarely need to be opened up.
As an interesting aside, Sturmey Archer hubs also have a 3 or 4 digit code on the shell, which lists the month and year the hub was made. The green on above says "5 74", or May 1974.