How to hook up another router to my home network?

Ok here's the situation. I have a modem/router (wired &wireless) from my ISP (Comcast) which my husband has downstairs in his man cave so he can play his game (Xbox, PS3) and have his Wi-Fi signal for his iPhone. Now I'm upstairs and only connected via wireless. My laptop gets an ok signal but my phone barely gets anything & this is all in my room which is directly above him, in other parts of the house it's virtually non-existent. We have another router that is our own. Can I hook it up upstairs so that my wireless signal is stronger up there? And if I can, will it affect his signal? God forbid the game lags, it will be a problem lol. So if anyone can help me, I'd greatly appreciate it.

Just get a wi-fi extender. This will increase the signal and therefore should get a better connection.

Yes. These days, you can configure both routers with a sort of bridged Wi-Fi network via WDS if your routers are new enough (support WDS). They will share the same SSID and I think the same passkey and channel. Read below. Routers are kind of an expensive way to do it, but they do provide a firewall for the internet jack. APs are less expensive.read your router manuals (it's on the cd's) to figure out how to set up WDS on your routers.

you can even set up a mesh network if you wish. If you have 2 comcast lines, you can have 2 routers connected separately, and 2 modems. They will be separate networks (you probably should not mix them together in any way).