Bike spokes typically don't require a lot of maintenance. They don't move or wear out and so there's not much you need to do with spokes other than check them occasionally to make sure none are loose and maybe wipe them down at the same time to remove excess grime.
To get a sense for if a spoke is loose, that is, if it doesn't have enough tension, take a moment to strum the spokes in your wheel, plucking each one individually with your index finger like you're playing a harp. The spokes on a wheel in true will all sound about the same tone or note when you pluck them. It's difficult to describe but will be easy to understand when you try it. A loose spoke will sound a much lower note, or will buzz, like if you pluck a guitar string with no tension in it.
Also, when you do this, turn your bike upside down or set it some way that you can spin the wheel and watch it turn freely from above. If the wheel seems to slither from side to side as it turns or rub against your brake pads here and there, you probably have spokes out of adjustment and the wheel needs to be trued.
With a spoke wrench, you can loosen or tighten the nipple in the rim at the parts that seem out of line to try to bring the tire back into adjustment, but this is a bit of a tricky process and sometimes best left to the pros at your local bike shop. I think they charge a whopping $10 or $15 bucks to true a wheel where I'm at, and that is usually money well spent.
The goal is to have a rim that is not only straight, without wobbles from left to right as it turns, but also perfectly round and no flat spots like an oval. When the rim is properly aligned by spokes tightened to the correct tension, people say the wheel is in true.
If you decide you really want to give it a whirl, I'd recommend the following guides to truing a wheel: