Skate bearings generally last a long time and require little maintenance. If you ride them in the rain or through some puddles then it might be a good idea afterwards to give them a strip and regrease just to stop them rusting too fast. Many people keep an old knackered set of bearings specifically for sliding and skating in the rain. Saves you rusting up those brand new bearings you just got for your speed board!
Take the nut off the axle and slide the wheel along the axle so that the innermost bearing is just on the edge of the axle. Using the same kind of motion as you would to open a bottle of beer, prise the bearing out of the wheel. Flip the wheel over and repeat.
Once you've got your bearings out of your wheels, you need to get inside the cartridges. If you're lucky your bearings will only have a single shield, but most likely you'll have to take one of the shields off so you can get to the balls and cage. With a rubber shielded bearing this is easy - just prize one shield off with a small screwdriver. Unless you are VERY careful you're probably going to damage the shield taking it off - but that's OK, you only really need one on each bearing. Metal-shielded bearings have a "C" clip round the outside of the race that you'll need to take off. On some bearings it is possible to remove the balls and cage from the race entirely for individual cleaning - but unless you really have nothing better to do it's not really worth it.
Next you need to get all the old crap and grease out of your bearing races. Avoid using WD40 - the best bet is to use methylated spirit or just soak the bearings in some solvent or alcohol. Lemon juice works well too! Soak your bearings in your chosen liquid try putting the bearings in a jam jar and shake the bejeezus out of them for about 2 minutes, then rinse them with some more clean solvent.
Regreasing:
Dry them off (hair dryers are handy here) relube them with a touch of oil or grease. You don't need much lube in there so don't go too crazy! The thinner your lube, the faster your bearings will spin, but the more prone to destruction they will be. Oil makes your bearings mega fast, but if any crap at all gets in there your bearings will be toast. Plus oil has a nasty tendency to spin out of the bearing at speed leaving your bearings without any lubricant, which leads to overheating bearings and melting wheels. Not cool… but maybe worth loOKing at if you really like cleaning bearings. On the other end of the spectrum is medium grease like the white stuff you can get at a bike shop. If you use this your bearings will be much more resistant to crap and should last a lot longer, especially if you ride in the rain a lot - but the flip side is that they'll spin slower. Really your best bet is a skateboard bearing specific lubes like Powell Speed cream or similar light grease.