In my experience there are two situations where people tend to get on the wrong side of the road:
After stopping for whatever reason. If you're thinking about something else when you get back in your car and start driving, you can very easily do the wrong thing based on your usual driving side. Visualise how you're going to start out (enter the street) before you start driving.
When transitioning from a narrow (perhaps a winding mountain) road to a wider one. This is particularly important if you are in an area with one lane bridges. Here in New Zealand, the road is often marked with a forward arrow in the correct (left) lane when the two lane road resumes.
It is also helpful to have somebody else in the car who is paying attention to your driving and can let you know if you're doing (or about to do) something wrong. Another pair of eyes definitely helps.
For lane changing, well I've never driven in India so all I know is what I've seen in pictures and videos. I understand the concept of "lanes" is not widespread. In the US, generally you can change lanes whenever there is a broken white line between the lanes (assuming both lanes are in the same travel direction). Signal your intention to change at least a couple of seconds in advance. Don't change lanes while going through an intersection.
There are likely many online driving tests for any particular US state that you intend to drive in. It might be helpful to run through some practice tests if you are unsure what you need to know. Most rules are the same throughout the country, but some states have particular rules you may need to know (rules that often vary are things like U-turns and right turns on red).