The type of clay that I've always used is Super Sculpey, which can be found almost anywhere that has some kind of craft section. Joann Fabrics is where I've been getting mine lately.
Clay that you can bake in your oven has been around for years, but it seems like the popularity has ramped up recently what with the social medias and diy shop websites and all. Through those sources I found several artists that really inspire me; I see their work and can't help but be envious and mystified by their skill.
Monster Kookies - The Mad Scientist of Polymer Clay (www.monsterkookies.com)
Beastlies - Adorable Mini-Monsters (www.beastlies.com)
Beat Black - Polymer Clay in It's Most Visceral Form (www.etsy.com/shop/beatblack)
Step 1: Tools of the trade
Royal Sovereign Clay Shaper Sets
I love these little rubber tipped brushes. They are just flexible enough to work on a surface like a tiny finger. These guys are kinda expensive though (a set of four costs about $30,) but they are absolutely worth it.
You know the pointy ones that they poke around your mouth with? They also work great for sculpting and you can get them dirt cheap from American Science and Surplus.
Wax Carving Metal Tool Set
Similiar to the dentist pick, these usual come in a set of a dozen tools with all kinds of odd shaped tips
As the name suggests, these tools are made from loops of bent wire ribbon. The edge of the wire cuts through clay and removes it from the sculpture and are useful for hacking out the subject's general shape. They can be used to create large grooves, or for shaving away small flakes of clay.
Kemper Circle Pattern Cutters
These small tubes behave like cookie cutters, but for clay. They are pressed down into a flat sheet of clay to cut a circle, which could be done with any metal tube, but these cutters have a clever button on top that lets you pop the newly made, clay disk out.
The classic style, hand crank pasta machines are perfect for pressing clay flat and for mixing colors. I've also seen people use these for making noodles, but you shouldn't do that after using one for clay.
I consider drinking straws and sewing needles essential parts of my tool set. Old toothbrushes can be carved into chisels and wire can be hammered flat to make knives and scoops. Plastic toothpicks also work very well as the ultimate multitasker.
A long while ago I was working on a zombie mutant thing who had exposed portions of muscle, I ended up gluing a half dozen sewing pins to a piece of wood to create a small rake. I then scraped the rake over the surface of the clay and smoothed it out with alcohol. The striation texture made the muscles look absolutely spot on, take my word for it (sorry, no pictures.)