Don't rely on your brakes to tell you whether the wheel is centered, since the brake often gets knocked to one side or the other when the wheel is off.
Have the bike upright, balanced on the front wheel. Put the wheel between the chainstays and the tire between the brake pads and get the chain into position. Hold the bike by the seat stays as you pull the wheel back into the dropouts. You should have to gently spread the dropouts by a mm or two. Once the QR is between the dropouts, put the wheel on the ground, grab it directly behind the chainstays and pull it straight back until you can feel it seat on both sides.
After you set the quick-release in the drop-outs, tighten it, then inflate the tire and then eyeball the rim in the chainstays near the bottom bracket. If it's off-center, then repeat the last step until it looks good. NOW check whether your brakes are centered. If they're off, re-center the caliper, spin the wheel, apply the brake, and make sure they're still centered.
Remember that late-model drop-outs have that little tab that means you will have to unscrew the quick-release to get the wheel off, and screw it back down to secure the wheel when you install it. You will have to do this by feel - the QR should be very tight, pretty much as tight as still allows you to throw the lever without totally wrestling with it. It should leave a mark in your hand.
Speed comes from what you put behind you. - Judi Ketteler