Young 3-year-olds are often balls of energy, constantly moving from one place to another. Combine their need for busyness with a color activity. Create a game by coloring individual pieces of paper. You can even have your little one help you with the process. Just make sure each paper has only one color. To play the game, spread the papers out over an empty floor space. Instruct the child to run and stand on a piece of the paper you call out. As an alternative, you could have them bring you the piece of paper, eliminating it from play as it's found.
Combine a game about colors with a way to challenge the three year old's memory. You may be able to purchase a color memory game or you can easily make one on your own. You'll need two index cards for each color. Make matching pairs by drawing the same shape outline filled in with the color. Because of the child's young age, you may want to limit the number of cards to three or four pairs in play at a time. Turn the cards over and then have the child overturn two of them in an attempt to match. Encourage them to say the names of the colors on the cards as they overturn each one. Once a match is found, remove the cards before continuing.
Take a color walk with your little one and turn learning into an adventure. Go for a walk around the neighborhood, in the woods or even around the grocery store. As you walk, talk about the different colors you see, encouraging the child to point to and identify the ones he can. Pick a new color to learn and make it the focus of the walk. Point out the new color as you pass objects, having him repeat the name. Make the game more interesting by making a pair of binoculars by gluing two toilet paper rolls together, for discovering the colors.
Teach your young 3 year old about sorting by colors that are the same. Give them a group of colored objects like beanbags or pompoms and instruct her to place all the identical ones next to each other. To help give them different containers that match the colors of the objects -- have them place the objects in the matching container.