You will do most things in Lao kip but it's easy to change USD and THB in any town big enough to have a decent sized market.
The exchange rate for Thai baht at the end of 2014 was between 246 and 250. For USD it was a bit over 8,000. I never felt ripped off and a few times felt the money changers could not be making any profit from my transaction at all. (The normal exchange has changed a lot over the past decade but I haven't changed money in 2023 to update the typical rates.)
It's much much easier than changing money in Thailand used to be, which could be a total pain. I never bothered trying to change money at a bank in Laos. If you want the best exchange rate it's always worth finding the money changers near the market, they will always have better rates than exchange booths in the tourist area, if there is one. Make sure you don't leave it too late. Money changers close in the afternoon before dusk except a couple in tourist areas such as by the fountain in Vientiane, where the rates may or may not be competitive.
EDIT The one time you will have to pay in THB or USD is if you want a visa on arrival, this was $40 for me one or two weeks ago and there was also a $1 fee for for outside normal hours and a ฿100 fee if you don't have a passport photo. The price in THB is higher than the price in USD so it's worth bringing dollars. They are extremely fussy about which USD they accept. Mine were perfect but not absolutely 100% mint and were rejected!
Vientiane has expanded a lot in the past decade since my original answer, and so has its tourist zone. There seem to be more money changers in more areas these days. An American friend uses a pharmacy to change money.
There are now no ANZ ATMs in Vientiane. I was able to withdraw 4,000,000 kip from an ATM at the JDM main branch. This may be more than you can typically withdraw from a random ATM in the country if what I read online is still accurate. Previously, ANZ account holders could avoid ATM fees by using ANZ ATMs.