Bicycle tubes typically use one of two valves to accept and release air--a Schrader or Presta valve. For most people, the Schrader valve is a straightforward proposition since it is the same as you find on a car tire. Presta valves are skinny valves that require some adjustment before they will let air flow in and out. Some bike pumps work on Presta valves, others don't, but there's usually an easy fix.
Look at the nozzle of your bicycle pump. There are a couple of ways to see if it is Presta-compatible. Read the area around the nozzle. Often you just need to flip a switch to move between Presta and Schrader compatibility.
Unscrew the nozzle if no written directive is present. See if there is a fitting inside the nozzle that comes out and has two sides. If there is, replace the fitting so that the end with a slight point is facing out. This side is designed to function with Presta valves. Some pumps require no adjustment whatsoever, working right out of the box with Presta valves.
Remove the valve cap from your Presta valve. Unscrew the tip of the Presta valve, moving in counter-clockwise direction, a few turns. Tap on the tip of the valve. If it opened enough, it will depress and you will hear air escape from the valve.
Push the nozzle of your pump onto the Presta valve. Using your thumb, push the lever attached to your pump's nozzle down, toward the pump's house.
Pump up your tire to the pounds per square inch (PSI) listed on the tyre's sidewall. Most pumps come with built-in gauges that tell you how many PSI are in the tire.
Lift the lever on the nozzle away from the pump's hose and pull the nozzle off of the Presta valve simultaneously. You will hear a noise--a poof of air, so to speak. This is normal. It is just air escaping from where the connection was released between the pump and valve.
Tighten the tip of the Presta valve by turning it in a clockwise direction. Replace the valve cap.
If you do not have Presta-compatible pump, buy a Presta valve adaptor from a bicycle shop. This adaptor screws onto the end of an opened Presta valve, allowing Schrader-only pumps to work with Presta valves.