The standard type of valve on most modern bike tires is called a "Presta valve" (sometimes called a 'French Valve'). Unlike Schrader valves, which are common on some mountain bikes and all car tires, these types of valves are built to handle high-pressure tires, since the narrower valve stem increases the strength of the tube.
Presta valves can be a little tricky to figure out when you are first working to fill one of them with air. The first step is to remove the black dust cover from the top of the valve. Set this aside somewhere it won't get lost.
Now, grasp the top of the valve and gently unscrew (turn to the left -- remember, lefty loosie, righty tighty) the brass cap at the top of the valve. This has to be unscrewed (it won't come off completely) in order to fill your tire with air. If you press down the top of the valve with the brass cap unscrewed, you should hear and feel air escaping (as long as there is pressure in the tire).
In general, the whole length of a Presta valve tends to be threaded. Usually, a lock-nut at the bottom of the valve holds the valve in place. Some tubes are smooth and don't feature this lock nut. Either style is fine, although it can be easier to inflate a fully-flat tube with a Presta valve with a lock nut, since the nut will hold the valve in place while you pump.
To inflate a Presta valve, remove the dust cap, unscrew the brass cap, slide a pump onto the valve as far as it will go and flip up the lever on the pump to secure it in place. Pump away until your tire is inflated. Then, remove the pump, screw the brass cap back into place and replace the black dust cap. You're good to go!