DO NOT start here! This will make you crazy! So often when I visit paint stores, I hear couples deciphering back and forth on what color they should choose. This normally ends with the man saying he likes all three of them and wants to leave the decision to her (mainly because he is tired of the conversation). Then the woman agonizes until she is forced to make her decision which in the end she normally regrets.
If you find yourself in a paint store looking at samples, take them home first. Paint may only cost $30 a gallon, but the process of painting isn't one that most people want to repeat.
Start by thumbing through magazines to find color schemes that are appealing to you: House Beautiful, Better Home and Garden, This Old House, Traditional Home, Veranda. If you don't subscribe to magazines, choose the longest line at the supermarket and indulge or collect photos on houzz and pinterest. The photos you collect will help you define whether you like a calm palette or love a lot of color.
Now that you have an overall sense of the look you would like to achieve, take into consideration what you already have. Pull colors out of your dining room rug, a throw pillow that you love, your countertop, or a beautiful piece of art. Collect some paint samples and take them home to look at the hues in your lighting with your furniture. A shade of gray that looks wonderful in the store my have a mauve undertone in your living room lighting or could look yellow when you lay in on your floor tile. For example, the 3 gray palettes pictured show different undertones when compared to the countertop sample.