Lift the wheel off the ground and give it a spin. You are watching for two things:

Lateral true = watch the wheel as it spins between the brake pads, the gap between the pads and the rim should remain consistent to within a mm or so. If you have disk brakes, you can put a zip tie around your fork or seat stay and trim it so that it barely clears the rim and use it as a gauge instead.

Radial hop = spin the wheel again and watch from the side using the top of the brake pad or your zip tie as a reference point. Watch to see if the top edge of the rim moves more than a mm or so in relation to your reference point.

Even when the wheel appears laterally and radially true, you should check spoke tension. Some people like to tap each spoke with a metal tool to listen to the pitch produced. I haven't had great luck with this and find that (for me) it is more accurate to squeeze pairs of spokes between my thumb and forefinger. If all the spokes feel tight and give approximately the same amount, you are good to go. Realize that, while your front wheel spokes should feel equal from side to side, on the rear the drive side will be tighter due to the offset required to get your cassette or freewheel between the stays.

There are some good videos and tutorials on wheel truing online. Stick with the ones from recognized authorities like Bicycling Magazine, Park Tools, or Sheldon Brown. With some practice, you can do a functional job of truing and tensioning with the wheels on the bike, using a makeshift work stand and a good spoke wrench. Make sure you get the correct size wrench as spoke nipples come in different sizes and using the wrong wrench leads to rounding off the nipples, which is a bad situation.

If there is a bike shop or co-op in your area that offers a wheel maintenance class, it would be time well spent.