Blimey, I just realised it's almost nine years since I went to the Oruro carnaval... doesn't time fly eh? My memory's a bit hazy but I'll tell you what I can remember.
The whole thing starts properly on the Saturday, with the Entrada (parade). Most of the streets in the city centre are closed to traffic and given over to the carnaval parades and the crowds. The parade itself is made up of a large number of groups from around Bolivia, each specialising in one of the traditional dances. The parade starts with the Diablada dance, which is the traditional core of the Oruro carnaval, and continues with dances such as Morenada, Caporales, Tinku and many more. Each group is followed by a group of musicians (generally either a brass band or traditional Andean instruments). The entire parade is on foot - there are no carnaval floats or other vehicles involved.
Meanwhile, the visitors will either have obtained a seat on the stands surrounding the parade route, or will be getting drunk around the main plaza. Water fighting is a big part of all Bolivian carnaval celebrations, and street vendors sell water balloons and water pistols in large quantities. If you're lucky with the weather it can be quite warm during the day, so getting soaked won't be too much of a problem (especially if you're drunk as well). Foreigners are right up there with schoolgirls as favourite targets of the local water balloon throwers, so expect to get wet. If you need to carry money/passport/documents, keep them in waterproof bags. It would be better to not to carry them at all if you have somewhere safe to put them.
Festivities continue throughout the night and then on Sunday there is a repeat of the Saturday parade. Sunday is more subdued than Saturday as many people are either still drunk or hung over and haven't slept. It's a good opportunity to catch the parade if you spent too much of the previous day drinking and water fighting.
I returned to La Paz on Sunday, so I'm not sure exactly what happens on Monday and Tuesday in Oruro. In La Paz these days are fairly quiet and the Tuesday is spent performing the cha'lla, where people make offerings and decorate their homes and possessions to encourage prosperity.
Oruro is not a big place so you should be able to follow your senses and find the best place to see what's going on.
It's a great experience - definitely the most enjoyable Bolivian carnaval celebration I have been to (I was in Bolivia for three carnavals).