Internet access is available in all but the most remote towns. Internet cafes are available in most tourist spots and rates are fairly cheap, ranging from 2,000-10,000 dong per hour. Connection speeds are high, especially in the big cities. Many hotels and restaurants provide free Wi-Fi or terminals for their guests.
If you bring your own phone as several providers offer mobile internet services (EDGE/3G) services as well for incredibly affordable prices. For example, Viettel offers unlimited (albeit slow) 3G internet / month for 70,000 dong as of June 2014 after purchase of sim card. Mobifone has better speeds though with a comparable "unlimited internet" pricing plan. Having mobile access to the internet for such a cheap price is really a no-brainer, as it opens the door to finding directions when you are lost, looking up hotel reviews, verifying reasonable pricing on services, using translation websites, and so on. This can really take the edge off of the difficulties of travelling to a new city.
Internet censorship is applied to small number of internet services. In the past, Facebook and Skype have been blocked. As of July 2014, Facebook still continues to be blocked in certain areas such as Hanoi. Which can be bemusing as Facebook is one of the de facto social networking websites used by locals. A quick Google search for solutions should help you bypass restrictions on banned sites quite easily. Other sites such as Gmail, YouTube, and Wikipedia are unaffected.