I doubt the filler level plug position will be in what passes for a drivers handbook these days, but you never know, Toyota handbooks are good with their more industrial products, i can't vouch for the car books.

Unless you want to invest in a Haynes manual, if one is made for your car, you would probably be able to find all necessary info where the level/filler plugs (usually but not always the same plug) are situated, normally half way up the side of the gearbox, and what oil to use, on the Toyota forums.

You will most likely need to jack the car up but still level unless you have a friend with a pit or lift, its possible but unlikely that the level plug will be accessible from above, remove plug and top up with the correct gear oil till it runs out, let the excess drain, refit plug job done.

Course it could be sensible if you're going to top it up to buy a larger can and give the box an oil change at the same time if one wasn't done in recent times as part of normal servicing...Toyota have never gone down the road of sealed for life cobblers (or more truthfully till it goes bang out of warranty as some other makers), a gearbox oil change will be somewhere in the service list.

Is there a way for someone inexperienced like me to check the gearbox oil level?

Try googling Toyota Auris gearbox level plug.