What does one need to host a 2-player game? I pay for an inexpensive website where I can post html files containing jars. Is that enough or does one need a site where Servlets are supported?
I have done a bit of Servlet programming on my home computer but home is a dynamic IP, and not anything anyone else can view.
Ah, just found the Kryonet resource. I will read up on this.
This mostly depends on what technology you want to use. Servlets are HTTP. Those are suitable for small non-real time games. For real time networked games, you will mostly need a dedicated computer/server and use sockets. Kryonet is an excellent choice for this.
If you want to use a computer at your home yet have a dynamic IP, I suggest you get a free subdomain name from DynDNS and check if your router supports DynamicDNS.
How about a peer-to-peer solution?
Cas 
Solving NAT-punch-through is a bit more advanced than ‘connect to server’. Besides, you’d most likely need a central server anyway for a lobby.
For the lobby, a PHP server would suffice.
Its easy to get a free service running it also.
you can run a dedicated server for free as well.
Wich Site? Would interest me.