Whatever you want to paint on or in. In the videos they paint on 16 x 20 inch canvases. I am painting in my 10 x 12 art journal with watercolor paper. Marie is using mixed media paper. If you do paint on paper, I suggest it's prepped first with gesso. The gesso will keep the paint from being absorbed into the paper fast and then dry.
Paint brushes. Here is a very inexpensive set that I got at Hobby Lobby in the children's craft area.
Optional: Paint spatula for mixing. In the videos they just use their brush to pick up paint and mix. Me I like using a spatula.
Apron and wear clothes that you don't mind getting paint on.