How to upgrade to an SSD on a Lenovo T520 laptop?

Do I need to buy Windows 7 or do I find a way to transfer it from the existing harddrive?

Can I run both hard drives alongside each other? Or can I only use the SSD?

Find the SSD you want that will fit in your laptop.
Buy a caddy that will take the SSD.
Get some software that can make a clone image eg Acronis.
Make a clone of your hard drive onto the SSD.
Physically install the SSD in your laptop.
You can now use the hard drive in the caddy for backups.

Laptops are usually made to accommodate only one hard drive. I'm not sure about the windows installation procedure but check on the back of your laptop if you have the product key and if the manufacturer, hence lenovo, provided you with a reinstallation disc.