The main route for Vietnamese Railways is the along the coast from Ho Chi Minh City to Hanoi and up to Haiphong. By Western standards trains are very slow (the Ho Chi Minh City to Hanoi express takes 30 hours) but most are much more comfortable than buses and a lot safer. The best way to purchase a ticket is through a travel agent or hotel. When you purchase a ticket ask which type of seat you are getting, some trains may only have hard seating.
Vietnam has an extensive bus network which covers almost every part of the country. Although tickets are cheap bus travel can be slow, uncomfortable and a lot more dangerous than travelling by train or air. The standard of driving in Vietnam is dreadful and head on collisions on the highways are all too frequent. Outside of the major cities the roads tend to be poor.
Major cities have metered taxis which are cheap and convenient. In Hanoi and Ho Chi Minh City they are usually found around the city centre particularly outside large hotels or shopping centres. Fares are shown in thousands of Dong so 25.0 on the meter is 25,000 Dong. A typical taxi journey costs from $4 to $8 and a trip to the airport around $15.
If you are planning a day trip then a car and driver is a good way to travel. The cost is quite low (probably $30 to $40). Most hotels will be able to arrange car hire. Most drivers don't speak English so you might want to hire a guide for the day.
You will find motorcycle taxis, xe om, everywhere in the towns and cities of Vietnam. They are a cheap and quick way to get around, make sure you agree a price before setting off. Also remember that driving standards are very poor and you will not be supplied with a helmet.
Bicycles are a great way to get around and by far the safest form or road transport. You can rent a bike in most major towns and cities for around $2 to $3 per day. Your hotel should be able to recommend a local dealer.
A cyclo or pedicab is a good way to explore either Hanoi or Ho Chi Minh City. Most cyclos are only big enough for one Westerner although the Hanoi version can seat two smaller people at a pinch. Expect to pay around $1 per hour. For short trips agree a price before you set off.