Linux detected my modem(finally!) and I then proceeded it to configure it with Minicom according to the instructions here. I got it configured, and can dial up to my ISP, but now I am trying to figure out how to get Lynx to use the connection. Any ideas?

Are you connecting to your ISP via PPP? If so, just fire up and lynx and you are on your way. If you are using minicom to make a direct dial-in connection to a terminal server on another unix box, then you will need to run lynx on the remote machine.

On connecting with Minicom, I get:

PPP session from [IP] to [IP] started...

On attempting to follow a link with Lynx, I get:

Alert! Remote host not found!

So: How do I keep the connection open? How do I get Lynx to utilize the connection?

I've never used minicom to establish a ppp connection, but as I'm finding out, there is even more than one way! Here's one that I found in a (old) book:
I don't know how close this is to what you're doing.

You could also write a chat script that will dial and start pppd for you...

If lynx can't connect, it may be that it can't resolve hosts...
look in the file /etc/resolv.conf
Does it have info for nameservers, domain and search?

Can you connect via IP address, or not even that? You may have to add a route, so packets can get out of your machine.

Try this:
lynx 64.23.37.23
If that doesn't work, try
ping 64.23.37.23
Let us know what the reults are with those commands...

I almost forgot what a hassle dialup can be, since I started using only WvDial.

Hope this helps a little.