How most does it customarily cost to get a automobile shipped to a city we live when we buy it online upon AutoTrader.com as well as how is it shipped? Like is it shipped buy sight or plane? How do they cost a automobile by a weight or distance of a car?

You DON’T. You buy it near where you live.
Unless you specifically WANT to pay more than its worth.
NEVER buy a car online sight unseen. You MUST go and inspect the car in person, drive it and then determine if the car is right for you.
Then you simply drive it home.
There are companies that will ship cars by truck, they don’t use planes or trains. It depends on how far they have to haul it but expect to pay a minimum of $250 to ship a car.
To address your specific questions, cars are typically shipped by vehicle transport companies on trucks that move anywhere from two to ten cars at a time.
There are many factors in pricing, but two of the major ones are the type/size of the vehicle and the mileage of the route. You can view more factors in the cost at: http://www.vehicletransport.com/about/faq.asp#Cost
The prices can be rather high. They can quickly turn a good deal into a bad one if you aren’t ready to add the shipping cost to the price of the car. The lowest you will likely pay would be $350 for a couple hundred miles. However coast-to-coast is easily over $1,000.
You can research vehicle transport companies on Transport Reviews.com (http://www.transportreviews.com/). When you are looking for prices to ship your vehicle you can use Vehicle Transport.com (http://www.vehicletransport.com/) to get price quotes from companies that are rated well by past customers.
Hope this helps. Good luck.