1. Tap "Menu" and then in the apps tap "Google Settings".
2. Inside "Google Settings", locate and tap on the "Ads" menu under "Services".
3. Next tap "Reset Advertising ID". (You will see the current Advertising ID listed here as well.
4. Be sure you confirm the reset when the confirmation prompt appears.
Once you reset the "Advertising ID", a new ID is displayed, immediately, on the same page. Since there is a new ID assigned now, advertisers can't link past actions to that device anymore. If only the "Advertising ID" was used for that, that is.
NOTE: You can, on the same page, opt out of interest-based ads as well. That tells apps not to use the "Advertising ID" for tracking purposes. It also tells them to only show regular advertisement, but not interest-based ads, on your device.