I booked a quick mileage run to Auckland that I've turned into a short 5 day visit. I'm on day #2, and survived driving on the left side of the road for the first time in my life. Driving from the airport up north to Orewa, I just kept saying to myself "keep left, drive left, left side" -- there are a number of habits this Californian has after 30+ years of driving :-)
For me the top tip to a right-side driver is pay attention to where the vehicle is in the lane. My biggest challenge has been calibrating my distance from the center of the road with it being on my right vs. left. Not sure why, but that and the little arrow/big arrow thing for right-of-way.
I'd also recommend reading the driver safety law book, I found that quite helpful in getting up to speed on the rules of the road.