Best Way to get into Qatar is by plane unless you want to drive through Saudi Arabia to reach there by car. Most airlines comes into Qatar like KLM, British Airways, Emirates, Kuwait Airways, Air India, Egypt Air,Gulf Air and of course Qatar Airways.
Taxis are fairly cheap but they have a day time and night tarrif (double the day rate). You can always rent a car but in this case read the danger section :)
Doha International Airport is small and quite crowded. However, it has around 50 scheduled arrivals daily, plus private and other plane movements. When I left Doha, Air Force Two, carrying US Secretary of State Colin Powell, was on the apron next to my Qatar Airways plane. Qatar frequently hosts foreign heads of state or government, such as the Saudi Crown Prince and Prime Minister, Abdullah bin Abdul Aziz
The airport in Doha is being improved to deal with the present fairly crowded conditions
I travelled on a nonstop flight with Qatar Airways (Business Class outward, First Class on the way back to London), which was excellent: for example, at Doha I was conveyed to the plane by a large BMW; on board, there was caviar and other luxury food and drink, together with excellent service. Highly recommended, though I cannot speak for the Economy section on the plane
A number of airlines call in at Doha: apart from Qatar Airways, one can use Gulf Air, Emirates, Saudia, British Airways etc. There are about 10 arrivals daily from London alone. India and around is also well served, with flights to New Delhi, Trivandrum, Colombo, Katmandu etc.
There is, in effect, no public transport in Qatar, bar a very few buses which transport country people into and out of Doha. Car hire is easy enough, but watch out for other drivers: Qatar (like Saudi Arabia) has a very high accident rate. Don't drink and drive here: penalties are apparently severe.
Doha traffic is congested at peak times, though it generally keeps moving, thanks to the excellent 6-lane highways which cover the city
Direct flights from London, Munich and many airports in arabic countries.
Doha is also convenient transfer airport if you are going to Himalayas (Europe-Doha-Kathmandu).
Qatar Airways is very comfortable, but the best in my opinion in Royal Jordanian Airways.
Very cheap taxi, but sometimes taxi-driver speaks only arabic and urdu.
If you drive be careful that you don't harm any camel.
You can drive into the country from Saudi Arabia, but almost everyone flies. Qatar Airways, a fairly new carrier, is very rapidly developing a reputation as being one of the best in the region. These people know how to pamper you! Like Emirates, in economy you get 17+ channels of entertainment on your own LCD screen, foot rests, and winglets on the back of your seat to lean your head against. The food is first-rate, too; it is anything but the loathsome plastic food that American carriers grudgingly serve. You'll get a hot snack on a short 45-minute hop.
By car or taxi. There are few buses and no railway.