You can't create (what you would think of) as an Internet connection using Hyperterminal, although you can get 2 computers to communicate over it - and this is probably the simplest way of communicating between 2 systems, but does not do an aweful lot unless you have additional software and/or someone on the other end. [ This is how "BBS's" used to work in the Pre-Internet and early Internet days]
You should be aware that when you make this connection the maximum speed will be no greater then 33.6kbit - and probably slower. If your provider uses VOIP for delivering the calls it will probably not work. (Even if your modems are 56k, you can't get get 56k unless one side uses special hardware and ISDN lines ].
In order to connect these systems to the Internet, we need to break the problem in 2 - The client (which is relatively easy) and the server (which is hard). On the client side you can use PPP dialup software which comes with Windows.
The server side is hard. You need a setup which while allow you to dial in to it and then you need to set up routing (and NAT). This can be done under Linux (and for low volume servers at the start of the Internet usually was). Here is one link I found on it. That said, unless you are an Linux expert it probably falls way into the 'too hard' basket. Note that this will just connect the 2 machines using the Internet protocol. You additionally need to set up NAT to route the Internet. An alternative to this would be to find a router which handles PPP. You may be able to find some ancient CISCO gear which can do it, for example this.
To answer the question about streaming video and implied question of real-world speed - this won't work. The speed you will get will be about 3kbyte per second, so a typical 1 megabyte page will take 5 minutes to load. This connection is really only good for the most basic Internet experience - pretty much email and text only-browsing and Instant messaging.