First, you need to create a directory for the game. Go to your dominions3 directory, open the 'savedgames' folder, and then within savedgames create a new folder with whatever name you want - but generally using the name of the game is a good idea.
So for example for the 'Alpaca' game, I created a directory 'dominions3\savedgames\Alpaca'.
When the game starts, you will be sent a trn file. You need to put this in the game folder you just created. You'll then be able to play your turn as normal using the 'Play an existing game' option in Dominions.
Once you've taken your turn and hit 'End turn', you should find a 2h file in the same directory that you put your trn file in. It'll have a name along the lines of 'mid_machaka.2h' (depending obviously on the age and the nation you're playing). This is the file that contains your orders, and you then need to email it to turns[ at ]llamaserver[ dot ]net. Obviously replace '[ at ]' with '@' and '[ dot ]' with '.' - I've written it funny so that the e-mail address doesn't get used for spam e-mails.
Within a few minutes you should get a receipt e-mail from the server (it checks its emails every five minutes). You can also see who's taken their turns and when the deadline is by looking at the website -
www.llamaserver.net.
If you decide to change your moves you can send a revised turn in to the server, and it will use the file it received most recently from you. It'll send you an e-mail to say so too.