Updated: May 7, 2019
There are some basic art supplies that every child should have. You probably already have a lot of them. Beyond that the possibilities are endless! Here is what you should start with:
Markers. I recommend the Crayola Ultra-clean washable type. These have ended up on my couch, curtains, floor and children. I can vouch that they come off easily.
Crayons. Good old crayola crayons work great.
Colored Pencils, and a pencil sharpener. If your kids are under 4 you may want to hold off on these, or put them away and only let them use them when you are supervising.
White paper. You could start with a ream of copy paper, and later upgrade to thicker papers for painting, and even special paper for watercolor. If it's in your budget buy a large roll of paper as well. I found some cheap ones at Ikea.
Construction paper in various colors.