Here's Alexa Chung in bangs and ombré hair color. Note how her hair looks as if it's growing out from blonde to brown. To mimic this look, ask your stylist for "baliage" hair color and only on the bottom two-thirds of hair. Baliage allows the stylist to paint swaths of color onto hair -- much better for this look than the typical pin-prick sized highlights that foils give you.
Learn more about this hair coloring technique in What is Baliage?