You should just be able to open Messages, and then from a new message, select the contact (who has a non-apple phone) and send them a message. You need to make sure that you iPhone is up to date with iOS 8 though, to be able to send it. The iPhone needs to be within range of the Mac computer as well.
You don't need to do anything special, apart from opening it. Im not sure if its available in the Public Beta versions, but the Dev GM Candidate 2 it is.
These are the requirements set out by Apple,
Requirements
1. Apple says that your iPhone, iPad and Mac will need to be on the same Wi-Fi network for these Continuity features to work.
2. You’ll also need to be signed in from the same iCloud ID on all these devices, which makes sense as you don’t want someone else’s iPad ringing if you get a call.
3.We’re not sure if these Continuity features require Bluetooth 4.0 LE support, as Apple doesn’t explicitly mention it anywhere on its website.
and thats really it. it shouldn't matter what hardware, but I think BT 4.0 would be a factor in it.
EDIT : From their site Apple - OS X Yosemite - Mac + iOS Continuity iOS 8.1 is needed.
These are the requirements set out by Apple,
Requirements
1. Apple says that your iPhone, iPad and Mac will need to be on the same Wi-Fi network for these Continuity features to work.
2. You’ll also need to be signed in from the same iCloud ID on all these devices, which makes sense as you don’t want someone else’s iPad ringing if you get a call.
3.We’re not sure if these Continuity features require Bluetooth 4.0 LE support, as Apple doesn’t explicitly mention it anywhere on its website.
and thats really it. it shouldn't matter what hardware, but I think BT 4.0 would be a factor in it.
EDIT : From their site Apple - OS X Yosemite - Mac + iOS Continuity iOS 8.1 is needed.
you're right 8.1 is also needed. Thanks
I now have 8.2 and can't get SMS on my mac after upgrading to Yosemite. Any suggestions? I can make calls. So that feature has worked.