Driving in Brussels is not that different from other European capitals. The city center is crowded and parking is expensive, therefore it is generally best to leave your car parked at your hotel and use the public transport instead.
The roads are in good condition and the infrastructure is well developed, so it is usually easy to reach various parts of the city. Avoid the center if possible and also avoid rush hours, when people either go to or come from work, since the traffic is moving very slow. A good GPS device is also a must, since not all streets and directions are properly marked.
Be aware that Belgians drive a little bit aggressive sometimes, for example the speed limits may not be always observed or you may find cars tailgating you. Do your best to drive safely, some scratches on your car in a foreign country is definitely not something that will make your holiday better.
An important thing to keep in mind is that you have to yield to cars coming from your right. This is the standard in Europe, but in Brussels you have to pay increased attention. Many times traffic coming from small streets on your right has priority, but you are on a large boulevard and you would have never imagined to yield to cars coming from such a small street. In most situations there are traffic signs that make it clear who has to yield, but when there are no such signs, yield to the right as this is probably the safest way to go.
Another aspect to keep in mind is that trams have priority.
Parking is not that difficult to find, but you have to pay. During night most parking places are free, but during the day they cost from €1 to €5 per hour. You can either choose an underground parking or try to find something on the street. If you park on the street, you will need a lot of coins to feed the parking meter and you have to put the parking ticket somewhere visible under your car windshield.
It is also not impossible to find free parking in the city. For example, around the Atomium there are usually a lot of parking spots that are free, unless there is some exhibition there.
All in all, it is not difficult to drive or to find parking in Brussels, but if you want to visit the city and enjoy it instead of focusing on the traffic, the best option is to leave the car in a parking and then use public transport.