No one sees your tires as often as you do, but you usually just overlook your tires as you get into the car. Fight this tendency. Get in the habit of occasionally examining your tires to make sure they're in good shape.
Once a month, check the air pressure in your tires. If you've never done this before, don't worry; it's not as difficult as it sounds. The correct tire pressure for your car is printed on the doorjamb of your car, and you can buy a tire gauge for less than five dollars. Unscrew the small valve cap on your tire, and press the gauge firmly onto the valve; the needle will pop out and display the current level of air pressure in your tires. All tires leak over time (generally around one pound per square inch per month), so you'll need to add air on occasion. If you're losing high amounts of air, however, take your car to a mechanic for professional inspection.
Next, whenever you check your tire pressure, you should also check the tread on your tire, which should be evenly worn on all areas. Your tire has indicator bars at the bottom of the tread grooves, and if those grooves are flush with the tread ribs, it's time for new tires. An alternative way to test your tread, however, is the Lincoln penny test. Take a penny and insert it (Lincoln's head pointing downwards) into the groove between the treads. If you can see the top of Lincoln's head, it's time for new tread.
Finally, use your senses of sight, touch, and hearing to determine if your tires are in good shape. Look for bulges, blisters, and uneven wear in your tires. Uneven wear, particularly a bald spot on your tire, indicates that your car's balance is off and/or that your tires need to be rotated. In any case, your traction on the road is vastly hampered. Next, use your sense of touch as your drive to check for excessive vibration or slipping that might be attributable to your tires. Finally, listen for high-pitched squeals as you drive; these squeals may indicate that your tires are underinflated.