Crafting a Dispenser will require 7 Cobblestone, 1 Red-Stone, and a Bow crafted from 3 Sticks + 3 Strings(Strings dropped from Spiders)
Red-Stone can be found deep underground in randomly generated cave systems. Normally around 15-20 blocks down from water level. If you start to find Gold,Diamonds,Lava or Lapis Lazuli, then you will most probably be near some Red-Stone.
You will then need to use a crafting table to craft the Dispenser.