The definitive answer is to consult Jarulf's Guide, which will tell you this and much much more. All axes are two-handed (3.1, page 17). All bows are two-handed (3.1, page 18). The Maul is two-handed, except when wielded by a Hellfire Barbarian (3.1, page 18). All staves are two-handed. The Two-Handed Sword (an actual item base type) and Great Sword are two-handed. Lesser swords are one-handed.
The quick answer is that if you try to equip a two-handed item, the game won't let you have the other hand busy. If the other hand is free, it will get a dimmed copy of your two-handed item to show that you are now using both hands. If your other hand is busy, you can't switch from a one-handed item to the two-handed item.