How can I tell if a weapon is one or two handed?

It's generally a matter of weight and weapon type.

One-handed weapons include daggers, swords (not greatswords), war axes (not battle axes), and maces (not warhammers). These will generally max out at 20 weight (with maces being the heaviest)

Two-handed weapons include greatswords (not regular swords), battle axes, and warhammers. Most have over 20 weight, but greatswords can weigh a little less (~15 weight).

Jesse Cox of OMFGcata also notes you can tell by the orientation of the weapon in the preview window:

• Two-handed weapons are tilted to the side
• One-handed weapons are shown vertically straight

You can see whether a weapon requires two hands if you equip it - if it's a one handed weapon it will say (L) or (R) (depending on which hand you put it in) and on two handed weapons it will show (LR) - just like with some spells that need two hands to cast (because it's too powerful for one hand).