Where to start
After logging in, you can join one of the multiple games which are running. Each game has a specific speed, where each action could take from a few seconds to even a few hours.
When you select a game, you can specify your home territory (country) and a colour to represent your army.
After joining the game, I suggest you open the map window... as this will show your current position and who occupies each of the territories.
How to play
All the action happens on the 'battle room' page... whereby you start by pressing the big 'Get Reinforcements' button. If you watch the territory list at the bottom of the page, you should see the number of battalions in your home territory increase.
Ideally you should keep pressing the 'Get Reinforcements' button as many times as you can... although there is usually a limit on most games, as some only allow you to search once per day!
When you have enough battalions, click on a territory name (in the territory list) and it will provide you with a list of neighbouring territories, with the ability to send your battalions to each of these territories.
After sending some battalions to a neighbouring territory, you will be returned to the 'battle room' where you can see a list of actions waiting to be completed. At first, it represents the battalions moving to the territory... but once complete, you will be presented with an 'Advance' link. This allows you to give the command to attack, conquer, or move, depending on the inhabitants of the destination territory.
The rest of the game is just about moving your battalions around and sending them to attack. It involves quite a bit of strategy, or brute force... and always remember to keep using the 'Get Reinforcements' button when you can, otherwise your army will slowly die out.