Creating an Account
How you go about creating a Starter Edition account depends on whether or not you already have a Battle.net account, which would have been created with any other Blizzard games you may own (eg. Diablo, Hearthstone).
If you already own a Blizzard game
If you have a Battle.net account then you can add one Starter Edition account to it. Any mounts, battlepets, achievements or heirloom equipment that you have unlocked on an existing WoW account will be available on a new Starter Edition account created under the same Battle.net account. Starter Edition accounts can be added at us.battle.net or eu.battle.net (If you are playing outside of your region, eg. on US servers while in the EU, then for some reason the battle.net website try to make an EU S.E. account on your US BNet account. You can create a US S.E. account by clicking on the 'Play for Free' button, then changing all occurences of 'eu' in the page address to 'us', and then hitting enter).
If you don't yet own any Blizzard games
If you are completely new to World of Warcraft and Blizzard games, then you can create a new Starter Edition account from scratch for either the US or EU regions (this will also creat a Battle.net account for you).