This is a really noob question, but I want to run multiple servers on one network. I know that I can only use one with my router. Could I get a switch, connect my servers to the switch and then connect my router? Would that work?

Why are you able to only use one on your router?

for the server to be accessible to the rest of the world it has to be under the default dmz server in the router, and there can only be one per router.

Sounds like a vendor limitation on the hardware you are using. Not that big of a deal, you can use an internal load balancer or switch of some sort behind the router to set-up your second server. I am not sure how well that could be implemented if your router only allows you to bind one. Normally you would request a second dedicated IP from your ISP and configure it on your router. So if you can only bind one to an external IP there is really no way for someone outside your network to specify which server they want to get to unless you do http host redirects or something like that.

I dont know what any of that means could you explain it?