How Much Lao Should I Learn?

Passing through -e.g. Vientiane-->Vang Viang-->Luang Prabang:
Don't bother. Everyone associated with the tourism (oops, travel) industry speaks at least some English. You can negotiate prices through a calculater. A nop (or wai, a bow with the palms pressed together) with a big "Sabaidee!" basically announces you're a clueless tourist. The Lao nop way less than the Thai. A smile and slight nod is fine when entering a store.

Staying about a month:
Learning numbers and some basic food vocabulary would be helpful but not necessary.

Staying a year:
Learn some basic conversational Lao, especially pleasantries ("this food is delicious" "you have a very nice home") and names of things you use every day. Learning to read and write would be a waste of time.

Over a year:
Learn to read and write. Yes, it's hard, but it's far from impossible. It's difficult in the same way learning anatomy is difficult: there's no trick to it, you just have to memorize a bunch of stuff. Remember, it's not a race, just do it at your own pace. Life will get a lot easier when you can use a dictionary, read signs and menus, and be able to correctly pronounce names. It's worth it just to see the shock on a local's face when you write something in Lao.