If you don't think your house has appropriate spaces for messy painting projects, I have some ideas for you to try...
If the kiddo is under a certain age, you can put her in her high chair and let her fingerpaint, paint with a brush and tempera or watercolors, or draw with a marker, and she won't be able to paint the walls with her paintbrush or touch the sofa with paint-covered hands. See the painting baby post on My Family Loves It about their daughter painting in her high chair (above).
The kitchen is generally more washable than the rest of the house. Depending on its size, you could put in a toddler-sized table in a corner or set up an easel in the kitchen for painting projects. You can even tape a large sheet of paper to the front of the fridge for drawing or painting.
If the weather is nice, set up a table in the backyard for painting and mess-making. You can always hose off the kids and the table afterwards. This photo shows Maia and Vivi outside at the "messy party" we had when we first started the art group. The messy party was inspired by a Mothering magazine article from a couple years ago.
Give the kid some fingerpaints or bathtub crayons and let him paint or draw while he takes a bath or before. We use both. Susan Striker, author of Young at Art, suggests mixing food coloring with powdered soap flakes and water to make an easy-to-clean up fingerpaint to use in the bathtub. After the kid paints in the dry bathtub, fill it with water, and wash the kid and the tub.
And then there's always the old standby of spreading newspapers or a dropcloth under your child and the art in progress...
Any other ideas for letting your kids paint and do other messy art projects if your house doesn't seem to have the right space?