The two most important rules concerning polymer clay are 1) Don't eat it, and 2) Don't burn it. Beyond these basic rules there are several more specific safety and usage issues.
1) Don't leave unbaked polymer clay on painted, varnished, or lacquered surfaces as it can damage the finish. (I learned this the hard way after I ruined a dresser). Once the clay is baked it becomes inert and this is no longer an issue.
2)Although polymer clay is rated as nontoxic it's not recommended for use with food. If you use kitchen tools for working with polymer clay those tools need to remain dedicated to use with polymer clay only. Never use anything made of polymer clay for utensils or dishware that will come into contact with food. You can, however, use polymer clay to embellish handles or other parts of dishes or utensils that won't come into contact with food.
These polymer clay covered wine glasses from TTE Designs are an example of how to safely embellish glasses with polymer clay. Please note that polymer clay covered items need to be hand washed and dried.
3)Be sure to wash your hands after working with polymer clay, especially if you'll be handling food. Pumice based waterless hand cleaner or hand sanitizer works well to dissolve polymer clay residue. Use soap and water to wash away the hand cleaner.
pumice based waterless hand cleaner
4)Never leave baking clay unattended as it can burn or scorch if you're not paying attention. Ovens, especially toaster ovens, don't always hold their temperature reliably. You should also always use an oven thermometer to be sure your oven is set at the proper temperature. I know my own oven is about 50 degrees off, so I have to set the temperature accordingly. If your clay looks like it is burning or smoking, turn off the oven and take the clay outside to cool off. Be sure to ventilate the room so the fumes can thoroughly dissipate.
5)When carving, dry sanding, drilling, or machine buffing polymer clay be sure to wear a dust mask and protective eye wear. The clay can be very dusty and you don't want to breathe that dust or get it in your eyes.
Heat Guns : Heat Guns reach temperatures much higher than those recommended for baking clay, making it possible to burn the clay. To start, clean your work area of any uncured clay and any flammable materials before starting to work with your heat gun. If you have long hair tie it back and make sure any loose clothing won't get in the way. You do NOT want to set yourself on fire! Hold the heat gun 3 to 5 inches away from the clay and keep moving it in circles until the clay is cured. Be aware that the tip of the gun will be extremely hot after use. Give the gun at least 10 to 15 minutes to cool off before storing it. And be absolutely sure to keep pets away from the heat gun while you're using it and while it's cooling off. The last thing you want is for your cat or dog to get burned!
Shiny Clay: Your cured clay can develop shiny spots when you use a smooth baking surface such as a ceramic tile. In some cases this won't have any effect on your piece, but it's easy to remove the shine if you prefer. Simply use a 1,000 grit or higher sandpaper and lightly sand the spot until the shine is gone.
Baking Thin Pieces of Clay: Since paper can curl when baking it can work better to bake very thin pieces of clay directly on your tile. You can also use a book to weight down the clay and flatten it after baking.
I hope these tips were helpful and will make your polymer clay adventures a bit safer!