|Your second router will connect to the first router and through it, the internet. It doesn't require a second, separate, internet connection.|
For information on how to add a second router to your LAN, click on my name above in my response and read my "how-to" guide titled (oddly enough) "Add a second Router to your LAN"
You will want to pay attention to the scenario where you have only one subnet and you connect the two router's "LAN port to LAN port".
If you're wanting to connect the second router to the first wirelessly, you will have to use "bridge mode" on one of them. I've never done it this way myself so can't tell you how to do it. I can only tell you to read the manual(s) that came with your router(s) and do some googling on the topic of wirelessly bridging two routers.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.