You can send someone a private message in a few different ways.
You can click on the member's screen name next to their review. Doing so open up a fly-out window containing information about the member and a Send Message link. Click Send Message and a blank private message will be pop up. From there, just fill in your message.
You can also send someone a private message from their profile page. Click the Send Message link under their name. If Send Message does not appear under the member's screen name on the profile page, it means that the member has disabled the messaging feature.
You can also visit the Messages section of your Profile. From there, click the Compose button to send a message to any member.
Important note: When you create a TripAdvisor account, private messaging is automatically turned on.