You usually start with the trainer in a starting city. For instance, horde is Brill, Under City, Orgrimar. I'm unsure of Alliance. But you just talk to the alchemy trainer and train in the items they have available.
umm... its easy... like if u start with leatherworking or engineering, anything really, u start of with a couple of potions u can create. Just check almemy under the "P" scroll, id put it on ur action bar. You will need vials: empty, leaded, crystal, or imblmed check the recipe