There are plenty of airlines flying into Ho Chi Minh City and Hanoi. Budget carriers Air Asia and Tiger Airways connect Vietnam with other cities in South-East Asia, while Jetstar flies to Ho Chi Minh City from Australia.
You can cross into Vietnam from China, Laos and Cambodia. From China, you can travel by train from Kunming to the border, from where it’s just an hour or so to Sapa. From Nanning there are direct trains to Hanoi. From the Cambodian capital of Phnom Penh it’s just a six-hour bus ride to Ho Chi Minh City. Alternatively, you can go from Phnom Penh into the Mekong Delta and explore that region before heading to Ho Chi Minh City.
There are plenty of domestic destinations served by air. If you’re in a hurry this can be a good (and not overly expensive) option, for example for the route between Ho Chi Minh City and Nha Trang. If you want to go direct between Hanoi and Ho Chi Minh City flying is by far the best option, and avoids a 36-hour train ride.
Trains can be slower than the bus, but are heaps more comfortable and a lot safer. The Reunification Express runs between Hanoi and Ho Chi Minh City and is a great option for long hops between the big cities (eg from Hanoi to Hue or Ho Chi Minh to Nha Trang). There are also overnight services between Hanoi and Sapa (highly recommended).
Buses go everywhere, and are incredibly cheap. But for journeys of more than four or so hours they’ll prove pretty cramped, bone-jarring and uncomfortable.