Check your bike's bearing surfaces: the headset, bottom bracket, and wheel hubs. Thankfully, modern sealed bearings only require you to inspect for any looseness or play. Most often, a headset is easily tightened, but some hubs, and most bottom brackets require professional training. "If you're not confident that you can do the job without messing it up," Zinn says, "then take it to a mechanic who can."
Headset: Put the bike on the floor and turn your front wheel so that it's perpendicular to the frame and squeeze the left-hand brake lever to lock the front wheel in place. Gently rock the wheel back and forth on the ground. If you feel movement, your headset bearings need to be tightened. Loosen the stem's steerer tube bolts, tighten the top cap bolt, and then retighten the steerer bolts. If the play remains, visit your local shop.
Bottom bracket: Grab the end of one of your crank arms (not the pedal) and pull it back and forth as if you were trying to free a drumstick from a turkey. You've already tightened the bolts that hold the crankset to the bottom bracket spindle, so if you feel any play, it's in the bottom bracket. Head to the shop and ask them to take a look.
Wheel hub: Remove the wheels and spin each individually while holding the hub on either side of the axle. They should spin smoothly with only a trace of play. Put your wheels back in the frame and check again for any side to side play. If any looseness you felt while they were out of the bike goes away, you're in good shape. If it doesn't, take them to a shop for a hub adjustment.