Installing OS X on SSD (installed on MacBook with broken HDD)

Hi, I have the macbook pro 13 inch model, mid 2012 - model a1278

I am not an expert at all, however I do have some experience changing hardware components.

A brief history

My HDD allready crashed once in the past, i bought another HDD on ebay with yosemite installed on it, i put it in the macbook and worked like brand new.

Now this HDD is failing. stuck at apple loading screen (grey screen with apple and loading bar) => shuts down at about 40 percent. I tried all the things mentioned on the web, I can not repair the disk (in disk utility using command R). I have error 8, the disk could not be verified completely. I guess the disk is broken. I tried to make a final back up but it shows an input output error...

Anyway, i have most of my files on an external hdd as back up. I don't really bother to fix this HDD (if this could be possible).

What I would like to do is to install a new SSD (replace the - probably broken - HDD) and get my macbook running again

I do know how to replace the HDD with an SSD. I am planning to buy the Samsung 850 EVO SSD - 500GB. This is a SATA III - I read on the internet the macbook cable is SATA II, but SATA III goes back to II so this would be no problem, I don't mind to buy SATA III, it seams the cheapest option anyway (150 euros).

The actual problem is that I do not know how to get OS X on this SSD. Do I simply install the SSD and install OS X via recovery mode (command R)? I read on the internet articles using a usb-SATA cable, others using a USB drive to put an OS X installer on it. I really don't have a clue how this works.

These articles handle about changing HDD to SSD on a working Macbook, mine doesn't. I do have another macbook air mid 2013 with yosemite on it. Or can i download an installer on the macbook air, put it on the usb, and use this on the macbook pro with the SSD installed?

I read the SSD has to be SUID - mac os journaled or something like that to be compatible, i believe a can do this using the disk utility.

As obvious don't really have a clue how to do this, someone who is willing to help me (as detailed a possible as i am not an expert)? Would be really appreciated!

(I didn't buy the SSD yet, nor do i have a SATA USB cable at the moment)