There is altogether little to say about how to get to North America, as air travel is almost the exclusive means of arrival. Every major city has an international airport, so you can comfortably fly into wherever your itinerary dictates.
If you want to see the whole continent, most people start in Canada to the north and work down, or Mexico in the south and work up. This can take a tremendous amount of time, which means more commonly backpackers will stick to the USA or Canada for their trip - there's more than enough to see in each.
You can expect the most stringent airport security when you fly into North America, particularly the USA, so be prepared to remove your shoes and belt, get confused over what liquids you can carry on, and maybe even have your whole body scanned. Alas, it's a small price to pay.
It's possible to enter North America overland through Panama, and there are a handful of ships that still make the epic voyage, but transoceanic liners are increasingly rare. So it's time get booking those flights.