The springs on a V-brake pull the arm away from the wheel. In order for V-brakes to be centered, there needs to be spring tension on both sides, and the tension on each arm needs to be equal. If the tension is uneven, the weaker side gets overpowered and yanked towards the stronger side (which means the weak side gets dragged against the rim).

In addition, all the parts need to be free-moving and free of friction, grime, rust, or sticky gunk. Lubrication on a few points helps.

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Order of operations for checking:

1.) Attempt micro-adjustment with spring adjustor screws. You can make the weak side stronger by turning its screw clockwise. You can make the stronger side weaker by turning its screw counterclockwise. Or you can do a combination of both.

If this doesn't solve the problem on its own, disconnect the quick release on the v-brake and check the components.

2.) Some bike frames have 3 different holes on each side where the spring can be seated - a top, middle, and bottom. (Top = most spring tension, bottom = the least.) Other bikes only have only one hole. If you have a multi-hole setup, check to make sure the springs are in the same set of holes on each side. If one were in the middle and one was in the bottom, the one in the bottom is going to have way less tension and get overpowered.

3.) Disassemble the brake parts, carefully examining how they fit together so you can put them back again. Make sure there are no rusted or grimy parts or anything. Kill nasty rust and grime with degreasing fluid and fine sandpaper. Lubricate anything that needs to be lubed, especially the little stud on the frame, with grease.

4.) There is a screw with a washer that goes into the arm of the brake and holds it onto the frame. While reassembling, keep the screw loose, seat the brake spring in place, and then feel the spring tension of the arm. Begin turning the arm screw in. As it starts to get tight, feel the spring tension of the arm. Sometimes the screw and washer will bind up or deform the washer to the point where it's crushing on the arm, restricting its movement. Check to make sure the arm can still freely move with tension as you tighten things up. If the washer seems deformed or smashed, flip it around 180 degrees, or pound it back flat with a mallet (best) or a hammer (serviceable). I usually grease the arm screw and the washer just for rust resistance, but the grease on the washer may help the brake arm move freely and prevent smashing.

5.) Make sure the cable routing & housing isn't pushing on the arms in some way which is preventing their movement.

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If all that fails (and it often does for new bikes) -- bend the spring! This is a last resort. Sometimes one spring will have been machined just a hair differently, and the angle of its wire will be just a tiny bit off. Such small differences can result in large differences in tension once mounted. I've heard from a pro mechanic that even some really nice, pricey bikes like Treks need springs to be bent before the brakes are perfectly adjusted.

Usually for spring-bending, I try to make the weaker spring stronger. Take whichever spring is weaker, hold it as if it were seated in the brake arm in the bike, and bend the longer, straighter part (the part that reaches up the brake arm, not the coiled part) away from the center of the bike using your hands. You will have to give it a strong yank to have any lasting effect. Bending the arm away from the center of the bike will make its tension engage sooner and stronger, and it will increase the overall tension strength on that side. If necessary to achieve even more tension, put it in a vise or something to hold it tightly and bend with 2 hands (or a tool you've grabbed it with), but don't go that route unless you're sure you need it.

Reassemble everything & put the brake arms back onto the bike. Leave the quick release off your V-brake for now. With your hands, push the brake arms towards the center and the wheel and then relax, feeling the tension on each side. Repeat several times. Does the tension on both sides feel even, or very close to it? If not, you need to fix something.

If/when you can do that test and feel the spring tension is very close to balanced, you're golden. Reattach the quick release on the brakes, and micro-adjust the tension on the springs with the screws until the arms are perfectly centered.

Hope that helps. If you have questions, ask!