Transport in Asia is usually easy to use, whether its long distance or just local. Most people speak at least some English and the region is extremely used to tourists so has created an extensive network for travellers, especially in South East Asia.
If you are tight on time it can sometimes be an idea to use domestic or other short distance flights between destinations, as overland travel in Asia, while cheap, can be time consuming. There are many discount carriers to choose from, and the key cities double as the key transport hubs. The national airlines are usually pretty good but beware of the really low-cost carriers as these can sometimes have dubious safety records.
One of the most enjoyable ways to travel through Asia is by train. Some countries are still without rail networks – most notably Cambodia and almost all of Laos – but most have pretty good routes in place. In places like China and Japan it can be incredibly efficient, and often relatively cheap.
Vietnam has a rail route which runs from Saigon in the south to Hanoi in the north, and the Thai capital Bangkok is connected to Chiang Mai in the north, Vientiane, the capital of Laos, and all the way to Singapore via Malaysia due south. Kazakhstan has railway links to China, Kyrgyzstan, Uzbekistan, and Turkmenistan, crossing some stunning scenery in the process. India, too, is well-equipped for passenger rail.
Buses are one of the most fail-safe means of transport in Asia: the combined network of tourist and local buses will get you pretty much between any two points you care to mark on a map. Most backpackers opt for the tourist buses, so called because they are slightly more expensive and comfortable than the local versions. Buses are often used for overnight travel, which creates a double win: a long distance is covered and you simultaneously save on a night’s accommodation.
Local buses are a bit more of a gamble. Many local drivers don't speak much English, so working out which bus goes where can be tricky. You're likely to have better luck in places like South Korea and Japan than elsewhere.
In South East Asia you’ll almost certainly hop on a boat at some point. This means of transport is the only way to reach the various outlying islands, which are hugely popular destinations to varying degrees. If travelling the Indochina loop overland, you’ll probably take a boat between Thailand and Laos, which is one of the classic journeys in South East Asia.
In most reasonably built up locations in Asia you'll be able to get a taxi. They're usually cheap, but always make sure the meter has been reset. If a cab doesn't have a meter, either agree your price before getting into the cab or find another one.