Any wobbly wheel with standard spokes can be "trued", so long as there no broken spokes and the rim itself is not bent.
It requires the proper size spoke wrench and a "truing stand". For more precise work you would also want a centering gauge, but that's not necessary in simple cases.
The "truing stand" can be a fancy $300 affair, an el-cheapo $50 unit, something you cobble up, or the bike itself.
The spoke wrench should be a good one. The circular wrench with multiple notches is a poor choice here, as it is often poorly made, does not get enough of a grip on the spoke nipple, and can hence can result in "rounded" nipples. Invest in a good wrench for your specific size spoke nipples:
Or, use a good-quality multi-size wrench like:
For newly built wheels many folks like to have a spoke tension gauge as well, but it's not necessary (and probably a distraction) for truing up a wheel such as in your case.
Truing is simple and complicated. It's simple if you only have to slightly tweak the wheel, and if you have a good understanding of the mechanics of the wheel. It's complicated if you're truing a newly-built or badly "tacoed" wheel, or if you don't understand it and and are trying to do it according to some "cookbook".
The basic process is to observe how the spokes run, tighten those that will pull the wheel "true", and, sometimes, loosen "opposing" spokes. To tell if the wheel is true you spin it in the "truing stand" and observe whether the two indicator fingers maintain a constant distance from the rim or move in/out relative to the rim. When you use a bike for a truing stand the brake pads (of rim brakes) serve as the indicator fingers.
Make adjustments in small amounts -- rarely more than one complete twist of the wrench, and more often one-half or one-quarter turn. Spin the wheel to check after each adjustment.
Be wary of "stuck" nipples. If the nipple will not turn on the spoke after applying a moderate force (the spoke will twist instead) you may have a seized nipple and going to a bike shop may be a better option. Rounding over a nipple is not the end of the world, but it's a bit of a pain, since the tire must be removed to get the nipple out and replace it.