To create a Neopet, you must first sign up for a Neopets account. Once you have an account and are logged in, click on "My Account" in the top toolbar and select "Create a Neopet" from the drop-down menu. You will then go through a step-by-step process in which you'll select your new Neopet's species, colour, stats, and name.
If you would rather adopt an existing Neopet who needs a home, visit the Neopian Pound and click on the Adoption door. Try adopting a Moehog! They're DJ Skellington's favorites!