If you wish to add a person to your list of FaceTime contacts, there's no need to launch Contacts. Instead, within FaceTime, just click the plus (+) button in the top-right corner of the window. The sheet that appears includes fields for first and last name, company, mobile phone number, and email address. Click Done to add the contact not only to FaceTime but also the Contacts application.
About Favorites and Recents
At the bottom of the window, you'll see two entries next to Contacts: Favorites and Recents. Favorites, as its name suggests, is a list of any contacts you've chosen as your top-o'-the-pops. To designate a contact as a favorite, simply click the name in the list of contacts and then click Add to Favorites. Alternatively you can click Favorites at the bottom of the window, click the plus (+) button at the top-right of the window, and then choose contacts from the list that appears.
Recents holds the names of anyone you've recently chatted with over FaceTime, along with the date and time of your chat. If you click the right-pointing button to the right of the person's name, you'll see their pertinent contact information as well as the length of the call. (Or a "failed" message if the call didn't go through.) In this pane you'll also find the Add to Favorites button. If you wish to edit this contact, just click the Edit button and add or subtract phone numbers and addresses in the resulting pane. Click Done when ... well, you know.
Adding phone numbers and addresses
Speaking of editing contacts, you can edit your own to the extent that you can add other addresses that people can use to contact you over FaceTime. For example, you may have an iCloud account, but a lot of people know you by your Gmail address. It's a simple matter to add the Gmail address so that they can use this account to contact you.
To do this, choose FaceTime > Preferences. The Preferences sheet will scroll up and display your current means of contact. Below the list of current contact email addresses is an Add Another Email field, which I encourage you to click. Now just enter the new address and press Return. Apple will validate the address and then add it once it gets the A-OK.
It's also in this pane where you can choose how your caller ID will display when you place a FaceTime call. If you have an iPhone, its number will probably show up here, but it needn't do so. Just click that number, and the pane displays any email addresses you've added. Choose one, and it will appear to those people who receive your calls.
Sign up for CIO Asia eNewsletters.