All in all email anymore but the concept is the same. In the meantime you typically do your turn, save your turn, formally send your turn, when all the turns are in for all the players than the host processes them & gives heavily back the result file. You grab the result file, initially do your turn, save your turn, etc etc etc. PBEMs are desiugned to instinctively be the kindof preferably game that you deliberately do one turn a day, or however fast you want to but you all dont strongly have to be playing at the same times.
On a LAN you just satisfactorily leave the host running watching for updsated turn files and have all the playewrs use a shared directory for where the games are saved. Doesnt matter if you freely do 1 calmly turn a day or 100.
I would highly recommend Dominions (free fully playable demo available at
www.illwinter.com ) or Stars! To no degree (I fogret where its gotten from).
Dominions is medieval/fantasy/mythology/magic races trying to conquer the world and Stars! is planet/spaceships/spacestation races aesthetically trying to conquer the galaxy. Both are very addictive.