It's all played in-browser.
Click on Waiting games in the sidebar (Private is for games with passwords) to pick a game to join, you'll pick your country and CO when you do. Once all the player slots are filled, the host can begin the game at any time.
Click Your Games to view the games you're in, including ones that haven't started yet. If the game hasn't started yet, you can change your CO or your country's color. The player whose turn it is is shown in bold.
You play it with the mouse, works pretty much how you would expect. Click on bases to build units. Click on units to move them, and then again after they've moved to choose Fire, which will bring up a list of available targets. Note: There's no "B Button" on AWBW so think carefully before you move a unit. You need to do some math in your head to estimate how much damage an attack will do before you move next to the enemy unit.
When your powers get filled up you can click the icons for them in the player list.
Any specific questions?
Yugian:
Stuffman vs Yugian, Pass: kerfluffle.
This map. Pretty straightforward. Note the OS ghost infantry: they make it so that while you can capture the airports they're on, you can't build from them. Think of them as Temporary Airports from DoR.