Could I use my webhost for a server?
Kind of -- in that you could cobble up something that allows a meeting place, where the server can gather the IP addresses of the participants, and then pass that info along to whoever hosts the game so their computer could do all the work and hosts the actual game session itself. If the game players would have to submit the game info itself in realtime through a webserver, it would be way to unreliable and slowfor the vast majority of the games -- you'd want one of the clients to play the server.
As far as finding game players on the internet: you really can't automatically discover them -- to do that you would need to scan the entire internet, which is:
a) ridiculously time consuming
b) a HUGE no-no, since people don't exactly appreciate getting portscanned
c) not a good approach
You -can-, however, have the game automatically submit a client presense to a webhost which can then be queried on where to find the other players... Or you could simply allow people to specify a hostname/IP address of whoever is hosting the game, so people can connect to other people they know and have a date/time for a game scheduled with. the first approach (having a website gather & keep track of the players that want to play a game) is probably the most user friendly and allows large groups of players to easily find one another... That's pretty much how something like BattleNet works, where you have a 'lobby' where people can meet, and start/join games in progress. but sometimes it's nice to have an option to just have a direct peer-to-peer game with another person if you already know their IP and don't need a match-making server.