How to install OS X on another HDD

Hi there,

I have a licensed compy of OS X Lion but I'm planning to put an additional SSD in my macbook pro '17, I'll keep the old one (current one) but I would like to move the OS to the SSD and use the HDD only for storage. So I have no problem installing the SSD but I was wondering how to install the OS on it as I don't have a hard copy (DVD) because I purshaced it via AppStore. So I don't have anything to boot from. What do you think should I do ?

I read a couple of articles and what I imagine is that when I install it, I'll boot from my old OS and than from the Disc Utility I'll install the OS on the SSD, than log in in the new fresh intallation on the SSD and will erase everything from the HDD. Would something like that work or I'm missing something ?

Thank you guys.