I'm not really new to Delphi or game programming but I know next
to nothing on programming for internet. I hope I can change
that.

Suppose I'd want to make a gameserver which could be used for
head-to-head real-time game, what would I need for that?
I already have some ideas about the problems I might encounter
but I was wondering if there were any (simple?) solutions.
Can anyone give me any advice, pointers, URLs?

Remco
http://www.onwijs.com/

planning, a good understanding of the protocol you wish to use, a good
understanding on the data your game need to send and plenty of time...

The best thing you could do is go on ID software web site and download the
quake 2 source code.

Another possibility is to delegate the game's netcode to the OS: IIRC
DirectX has a module for that. You'll still need to have a good idea of
what you are doing, but you can probably cut the dev time quite a bit.

Good luck,
stephane