If you are specifically looking for a river rock, the best place to look is a river bed. You can find rocks that have similar qualities at creeks, lakes, and on beaches. You can choose any rock that appeals to you, but rocks that are smooth are ideal for painting. Weathered rocks that that have been in the water for a long time are great for painting because they have tumbled, which has left them smooth and rounded. You can't take rocks from state and national parks. Be careful when you are searching for rocks. Do not get too close to the water unless you are sure that you will be safe or have someone watching you. Prepare the space where you will be painting the rock. You can paint anywhere you like, but a table or desk is ideal because it gives you space. Make sure to protect your work surface. You can lay newspaper or paper towels out so that paint doesn't get on the table. Consider recycled empty cereal boxes for a green alternative. Cut the box open on the side and unfold it. The inside has a nice solid light gray color. which gives contrast for your painting design, and the material is stronger than paper towels. There is also no risk of ink smudges from the newspaper.

Summary:
Find a rock. Set the rock out on a table.