The aim of the Sims online is to become the most popular character, and also to have the most popular house (houses earn populariy points when people visit them). If fact the game-play is open ended, so really you can make your own goals. For many people the Sims Online is just a place to meet other people, much like a three dimensionsal chat room.
In the online version of the Sims you have more of a direct control of your character than in the offline versions, though you still need to pander to their needs as in the previous games. Also you need to work and build skill points, which can get a bit repetitive at times, but is necessary if you want to buy a nice house. As a result, some players don't really bother and just mooch around other peoples' houses (especially in the free trial!), chatting and interacting with other characters. This is never usually a problem, as it adds to the popularity of the visited house, but there are a few Sims players who like their own privacy too much and will make it clear that you're not wanted there.
For the free online trial, the first thing to do is meet up with some other people. Interaction with other Sims Online players is such an important part of the game that it would be a shame to miss it by spending all of your time working and gaining skill points. You will be able to pick up some good tips from more experienced players too, and you can team up with them to work on skill points or employment, which will allow both (or all) of you to progress faster.
At the moment the economy is undergoing a changeover, whereby you can now buy Simoleons to take into the game (989 Simoloens for a dollar); this is called Cash-In. Soon EA will be introducing a feature called Cash_out, whereby you can exchange your earnt Simoleons for real-life currency, through Paypal. At this point the game is going to take on a different aim for many people, in that it will be possible to earn money from playing it.
It is also possible to create your own clothes and items for the game, so many people go online simply to get their stuff seen. Yay!