** Using WeBWorK **

I found my IP address by following your attachment. I typed
<my IP address>/webwork2 and it worked on my current laptop. Then I got on my old laptop and typed <my IP address>/webwork2 and it worked on there as well. When I typed localhost/webwork2 it worked on my current laptop but
not my old laptop.

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Sounds like you have the server on your new laptop, but not your old.
It seems though it is working as a server.
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I noticed another thing. The site <my IP address>/webwork2 worked on my old laptop when my current laptop was running Ubuntu. However, when I boot into Windows 7 the site <my IP address>/webwork2 did not work on my old laptop. As well, when I typed in <my IP address>/webwork2 in Windows 7 on my current computer, it did not work either. But, when I boot back into Ubuntu <my IP address>/webwork2 it did work again.

Does that mean I would have to have my computer on all the time (in Ubuntu) in order for students to access my server?

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Although you have me a little bit confused, the answer is yes. Servers need to be plugged in and running all the time. You old computer seems a good candidate for a server, sure beats the garbage. How old is it?

Presently I am running my "production" server of a used "off-lease" dual-core IBM computer that I paid about $165 for. It stays plugged in and continuously runs the UBUNTU (webwork) server.
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How do I know if students would be able to access my site or not? I think you mentioned that 192.168.1.101 was your local IP address. Does that mean only people local to you could access http://192.168.1.101/webwork2 ? Would I need a public IP address?

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Everybody has a public IP address somewhere. What kind of service do you have? Did you buy the router yourself at a store. If so defaults are typically admin,nothing or admin,admin. Typing the brand name into google "D-Link","Airlink" etc may yield the defaults.

I've noticed that fiber offers a free router included. I suspect that this is two devices in the one box. The same ideas apply?

Don't reset the router too quickly (there is usually a recessed button for this somewhere). Routers contain usernames and passwords for services that you have purchased from your provider. Unless you have this information on hand (it would be a scramble to find mine) you will end up with no internet access. This would all be the sort of information your service provider provides when you purchase your service.
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How do I know if students would be able to access my site or not? I think you mentioned that 192.168.1.101 was your local IP address. Does that mean only people local to you could access http://192.168.1.101/webwork2 ? Would I need a public IP address?

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There are millions of little networks that use IP addresses (locally) of the form 192.168.xxx.xxx These addresses do not go beyond your front door. Students outside this very small network cannot get access to you.
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When I go to google and type "what is my IP address", it tells me my public IP address. But, when I type
<my public IP address>/webwork2 it requires authorization. I have to enter a user name and password which I do not have. Do I need to get the user name and password from my internet provider? Or, will my local IP address suffice?

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The question is: who or what is asking? Can it be your router??
The question on my mind is: How was your service set up?; are there other persons involved in that setup (passwords on the router, etc)?; are you part of some larger network??
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Hope this helps.
hp