Physical Danger
Paint can be dangerous. Oil paint is natural and non-toxic. The acrylic polymer emulsion used to bind acrylic paint, however, can be highly toxic. Don't eat it. There are particular colors that have toxic substances such as genuine vermillion, genuine Naples yellow, tin yellow, and flake white. Lead pigments are also not good for you. Make sure that you use them in an area with plenty of ventilation and again, don't eat them.
To be sure that you don't ingest paint, don't drink or eat while painting. Don't stick a paintbrush in your mouth. Obviously, keep pets away from your paints. And definitely don't chew your fingernails.
Some people use mineral spirits, denatured alcohol, or turpentine when they use oils. These solvents are flammable. Avoid using them next to your stove or a flame. Shmoop knows this may cut into the romantic images of painting by candlelight, but safety comes first. Keep open containers with solvents away from any flames. Pretty easy.
Painting is as dangerous as cleaning the bathroom. You'll use some chemicals, but as long as you don't taste the toilet bowel cleaner or leave it near an open flame, you'll be fine.