Does anyone know how to use this App

The Help menu "Messages Help" will "help" you setup and use your Messages app.

I think you have to set up your Apple account to make Messages work for you.

To: gets the phone number that you send your message to.
enter the message. Send it.

 

Without an iPhone you won't be able to use it for texting. You can use it along with your AppleID to send messages to people with iPads, iPod Touches and iPhones, though.

 

Ah - so, just to confirm - it is not possible to text from OS X Messages app unless you have configured your Mac with an iPhone/iOS device, and that you also need connection to that iPhone to be able to send messages to an Android phone.
And that's the only way to message from OS X to Android (via an iPhone/iOS device) (?)

 

You can also use it for messaging with Google Hangouts users, I do it all the time. You just have to add your Google account in the Internet Accounts section of system preferences. I have both a Google (Gmail) account and a Google Apps account set up on mine.

 

You could use Whats App, Facebook messenger etc

But if you need to send SMS you need to setup Text Msg forwarding on an iPhone