Its size has necessitated that transport in North America is amongst the very best in the world. It's a massive continent, but its tremendously easy to get around, even if cheaper options will take a fair chunk of time. When planning your itinerary for North America you need to take the continent's size into account, and be realistic about what you'll be able to see in the time you have.
This is by far the quickest means of getting around North America. Every major hub has an airport, and from these its usually possible to reach a smaller regional airport if you're staying somewhere more remote.
It's also the most expensive way to travel, and for most internal flights you'll pay at least $200 for the pleasure.
Trains aren't quite as prolific in North America as they used to be, having been overtaken by air travel and a penchant for cars. It's still a good option for travelling between cities in the Northeast Corridor, railway linking Washington, D.C. to Boston, stopping at Baltimore, Philadelphia, New York City, New Haven, and Providence in between. It's also a decent option in California and parts of southeastern Canada.
Elsewhere on the continent trains are sporadic, and usually won't prove cheaper or more convenient than travelling by car or bus, particularly in Mexico.
North America was built for cars. Canada and the USA are riddled with well-maintained highways that in turn are dotted with food stops, gas stations, and motels. This is why these countries are the ultimate road trip destinations. Be aware that driving anywhere in North America can take a long time. To make it across the continent in a week you'd have to drive hard without stopping to see much along the way.
It's relatively easy to hire a car in North America, and insurance purchased in either the USA or Canada is usually valid in the other, but this is worth double-checking. If you're travelling to Mexico, make sure your insurance covers it.
Roads in Mexico aren't as well-maintained across the board, and in more remote areas you may encounter battered tarmac or dirt tracks. Still, you're unlikely to be aiming for somewhere that can't be reached on four wheels.
If you don't have your own car, buses are usually the cheapest way to travel long distances in the USA and Canada. You can get to most places by bus, but it really will take a hugely long time and can be incredibly trying on your patience/buttocks.