Frame balancing is honestly one of those things that seems mysterious until you actually do it, and then you'll wonder why you were ever worried about it. The core idea is simple: your quadcopter's center of gravity needs to be directly in the middle of the frame so the flight controller doesn't have to work overtime compensating for weight imbalances. When weight is off to one side, your motors end up fighting each other constantly, which burns battery faster, makes the quad twitchy, and can cause crashes that might have been totally avoidable.
The most straightforward way to check balance is the needle method, which costs almost nothing. Get a metal needle or a toothpick and balance your quad on the tip of it like a seesaw. Hold it under the center of the frame (you're aiming for that point equidistant from the motor arms) and see which direction it tips. If one side dips, that side is heavier. You can do this with the battery installed or without, but I'd recommend checking it both ways. Some people use a balance beam made from a ruler balanced on a pen, which is even more stable.
Once you identify which side is heavy, you've got a few options for fixing it. The easiest approach is repositioning your battery. Your battery is usually the heaviest single component, so moving it slightly left or right within its velcro straps or battery holder can make a huge difference. Even shifting it a centimeter or two sometimes does the trick. If that's not enough, you can add small pieces of lead weight tape to the lighter side of the frame. Most racing pilots keep a roll of this stuff in their pit box. Another option is removing unnecessary components from the heavy side if there's something you don't actually need, but that's usually a last resort.
I'd also mention that slightly nose-heavy is better than tail-heavy, though you want to avoid extremes either way. A nose-heavy quad will fall forward naturally and is easier to control, whereas a tail-heavy one feels sluggish and unpredictable. Some experienced pilots prefer a barely perceptible forward bias, maybe two or three grams, but that's getting into the weeds.
The process usually takes ten minutes tops. Do it before your first flight and then check again after you've crashed a few times or swapped out components, because changing your motor arms, adding a camera, or upgrading your PDB will shift that center of gravity.
