Lets say that I have a Linux box that I made into a router, what do I do if I want the router to display a terms and conditions/consent agreement page with a button that says I Agree before they are able to use the internet. A lot of small businesses use them and so do bigger stores with communal WiFi, I just want to know how to do it. With programs like Apache, (if required, Squid), and if I am assuming right about the workings of it, can I get it to work with Ruby on Rails? That last one is optional, How do you create the basic form.

There are a bunch of those already written, usually they are called "captive portals". For example:

https://coova.github.io/
https://github.com/wifidog
https://packetfence.org/

There may be a few others. There used to be one called NoCat (has since merged into WifiDog) that I used ages ago, and it worked very well. I can't say how these solutions work today, but I think it might be easier and perhaps more secure than building your own.

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I assume that answer is correct.

"How do you create the basic form"

They usually use a web page. Millions of ways to make a web page. If you have open/libreoffice then you can just save as web page.