If you've just moved to the United States from the UK, Japan, or another country where the cars have the steering wheels on the right, don't worry too much about whether you'll do well on the road. It's a lot easier to adjust to the new setup than you think. That being said, there is a short adjustment period that you'll go through. It's best to confront this head on -- no pun intended -- so that you can continue your journeys with confidence.
Orient Yourself Immediately
If, when you get your car, you can sit in it for a few minutes, do so, and get used to where everything is. Note the locks, the emergency light button, the layout of the gearshift if you rented a manual transmission (which is rare, but possible, in the United States), the pedals (which will still be in the same order as the pedals in a right-hand drive: clutch on the left in manuals, brake in the middle, and gas on the right), and even the radio. You don't want to fumble to find a control while you're actually on the road.
If, when you pick up the car, it's left waiting for you in a lane where other cars will need to pass through, carefully drive the car to the nearest parking lot or quiet street, and then do your reconnaisance.
Remember the Center Line
As you start driving -- on the other side of the road, remember -- keep the center of the lane in mind. You're going to automatically drift over so that your perception of the lane matches what you're used to; in other words, you're going to want the right side of the lane to be in front of you. When you're sitting on the left side of the car, this is bad. Keep your attention on the center of the lane and keep the left side of the lane in front of you.
The Worst Is the Side of the Road
You'll get used to driving the cars within a short time. A more pressing concern is remembering to drive on the correct side of the road -- if anything's going to trip you up, it's that. So take a few moments to plot out your exit from a parking lot so that you know the correct lane to end up in.
If you have other questions, you can call a local driving school, such as Morgan School Of Driving Inc, and see if they have any refresher courses for drivers that you can take. These will also help you get used to the driving rules in your new city, which can be very different from those in other countries.