With many transport options, you'll find good local travel agencies in every tourist stop in Vietnam, all ready to book your plane, bus, and boat tickets or to rent cars. Competition among service providers works to your advantage, and you can find affordable deals for getting around with just a bit of shopping.
It's a good idea to fly the longer hops along Vietnam's length: from Hanoi to Hue, from Danang to Nha Trang, and from Nha Trang to Ho Chi Minh City (or vice versa). Vietnam Airlines runs the most domestic routes in Vietnam, while budget carrier Jet Star Asia offers healthy competition on the tourist routes (namely to-and-fros btw. Hanoi, Ho Chi Minh City, Danang, and Nha Trang). Domestic departure tax is included in most fares.
If you've got the budget for it, going by car is the best and safest way to see Vietnam. Self-driving is unwise. There are rules on the road, but to the uninitiated, driving is chaotic. Your international driver's license holds up -- in fact, any piece of paper with English writing will do most of the time -- and right-lane driving might look familiar and easy to some, but that's where the similarity ends.
Turn it over to a driver, available for hire anywhere and for as little as $10 per day. Most hotels will rent wheels for day trips at inflated rates; budget hotels and guesthouses offer the best rates. Budget travelers often pitch in for a rented car between sites (from Hue to Nha Trang, for example), where going by private car means you can set your own schedule and stop at places like Bach Ma National Park, Lang Co Beach, and atop Hai Van Pass.
The Reunification Express runs the entire length of Vietnam's coast -- from Ho Chi Minh to Hanoi, with routes out of Hanoi to the likes of Sapa, Lang Son, and coastal Haiphong. Riding the length of the country takes nearly 40 hours. The most popular hops are from Hanoi up to Sapa, where special luxury trains with dining cars cover the route, or from Hanoi down the coast to the old capital of Hue, and from there to Danang (less popular) or all the way to Nha Trang and Ho Chi Minh. Improved road travel is making the train obsolete in most parts, except for the mountainous far north. There are a number of classes, from third-class hard seat to air-conditioned cushioned seat to sleeper, but in general the more comfortable seats are affordable. Be warned that you need to book trains a few days in advance, especially for weekend travel. Popular trips to Sapa are best organized through a tour company (for a small fee) from home or well in advance when on the ground in Vietnam.
Local buses are either a nightmare or a delight, depending on your expectations. If you're prepared to be the main character in a piece of bad, chaotic performance, then your appetite will be pleased; if you want grist for the travel journal, you will find it; if you want to get somewhere efficiently and with all of your sensory nerve endings intact, you will be disappointed.
Local buses depart from stations usually a good distance from the town center (it usually requires a ride on the back of a motorbike taxi to get there), and station touts are all over you, pulling you this way and that (this is the best piece of "bad performance art"). Buses leave only when full -- and "full" means that everyone is uncomfortable, two to a seat, produce hanging, bags under your feet and, bird flu be damned, chickens in bags and on people's laps. Just when you think the bus is completely full, when not one more person could possibly squeeze in, the driver pulls to the side of the road and, like a circus clown car, the bus swallows one more body. All buses honk wildly as they navigate the chaotic traffic of Vietnam's bumpy roads, and all transport travels at a lumbering 50kmph (31 mph).
In the bigger cities and on longer routes, you'll find regular schedules and bus stations with ticket booths and marked prices, but when you're out in countryside, you often have to negotiate a price with the driver or bus tout -- a frustrating operation when you just want to catch the @#%# bus. It is a real visceral adventure, and going by local bus is the best way to meet Vietnamese people and learn the local language, but it can be too overwhelming for some.
One good alternative is to buy a ticket with assigned seat on the small air-conditioned minivans that ply most major routes in Vietnam (the Mai Linh Express is a reliable option). Ask at any hotel front desk, and expect to pay often double the local bus price (still very affordable) and ride in relative style among locals but without the hassles.
The "open tour" ticket is a way to plan your overland travel all the way down the coast of Vietnam; it is a one-way, multistop ticket, and you can catch buses from each town going from Hanoi south, all the way to Ho Chi Minh City. It sounds like a great idea, and folks in the sales offices will regale you with tales of ease and comfort as you explore the length of the Vietnam coast, but don't be fooled: These are rock-bottom budget tours, and though the buses are usually in pretty good shape and have air-conditioning, it can be a pretty unpleasant cattle-herding situation among lots of complaining backpackers. Buses stop only at big tourist-shopping complexes, and you get little interaction with locals. That said, these tour buses are good for short hops between cities, but I try to mix it up, catching the train where possible (especially on long hauls from Hanoi to Hue or Danang to Nha Trang), and even getting together with fellow travelers and hiring your own car for a day along the coast (not much more costly). Don't be taken in by the easy "open tour" ticket, as, for just a few bucks extra, you can buy individual journeys from each town as you head south.