To search, simply select "Contacts" or "Messages" on the left-hand side of the page, and search away using the search bar above those options.
To search for a Contact, you must be in the Contacts tab. You can search by first name, last name, phone number or tags. You cannot search in the Messages tab for a Contact.
To search in the Messages tab, simply click on the search bar and search for any Keywords in your Message. This will bring up the Conversation and highlight where those keywords are.