Laos' laid back capital has been described as looking more like a collection of villages than a big capital city. It is growing, but still has a slower pace than the cities of its neighbor to the south. It is still a small city, with not a lot of major sights. You can see most of what "must" be seen in less than a day. However, there's an atmosphere in Vientiane that appeals to many, and any trip to the city should last for a few days at least, to give you time to unwind and relax.
You can see most of the main sights on foot, since they are within a short distance of each other. A good place to start would be the Presidential Palace. From here, you can visit the former home of the Emerald Buddha, the Ho Prakeo, and Wat Sisaket before strolling up Lane Xang Road to the Patouxai, Vientiane's own triumphal arch.
All that walking will make you hungry, and Vientiane's restaurants provide an interesting mix of French and Asian influences.
The area around Vientiane has probably been settled since at least the eighth century, but it wasn't until 1560 that the Lao king Setthathilat moved the capital here from Luang Prabang. The city was attacked and overrun many times during its history, by Burmese, Chinese, and last but certainly not least by the Siamese, who more or less leveled the city in 1828.
The French arrived in 1867, and found the city abandoned. They eventually established Vientiane as the capital of an administrative division of French Indochina, and rebuilt the city. The name "Vientiane" is a French corruption of the Lao name for the city, Wiang Jun, which translates to "sandalwood fortress." The French presence lasted from 1899 to 1945, and most of the city's small number of colonial buildings date from this time.