If your bicycle has a presta valve inner tube, you'll know it because it it much thinner and longer than an ordinary bicycle valve. The PrestaValves are common on mountain bikes and high performance road bikes.
You really have 3 options for inflating a presta-valve tire:
1) Buy a presta valve pump (see below).
2) Buy a presta valve adapter. This is a small device, usually made out of brass, that will convert a presta valve into a regular schrader valve (the kind on most cars and bikes). Then you can use any old pump! Just a few buck for the adapter is much cheaper than a new pump.
3) Drill out your presta rim and use a schrader