To access MPGE and to play AOA, you must be registered on the site.
For instructions on that, see the Registration page.
Logging on and issuing a challenge are the same as how this is done for FBS
Once you have issued the challenge, your opponent has the ability to accept or reject that challenge.
If the challenge is accepted, the person being challenged gets to set the parameters for the game.
The person making the challenge will see this:

The person being challenged will see this settings page:
What do each of these settings mean?
If the Process for selecting dogfights is Random, then the random selections are presented to the challenger to be accepted or rejected.
Here, five random dogfights will be played, with no limits on the books or matchups between sides:

Here is one sample set of dogfights that could be selected:

If the dogfights are planned, then the challenged player will get a screen allowing them to make choices based upon the planned options selected.
If neither of the “Use the same book for every dogfight” or “Will both sides use the same book series” options are selected, the screen will look like this:

If only the “Use the same book for every dogfight” is selected, you will see this page:
All five dogfights will have the same matchup between planes.
If only the “Will both sides use the same book series” is selected, this page will be displayed:
The Germans and the Allies will both use the same planes for each dogfight.
And if both options are selected, this is your only choice:
The Germans and the Allies will both use the same planes for all dogfights.
Once the selections have been made, the challenger will get a confirmation page with the ability to accept or reject the chosen game settings.
For example, if the challenger has made these selections:

And then makes these choices:

Then the challenger would see this confirmation screen:

If the game selections are accepted, then the first dogfight will begin. (If the selections are rejected, the challenged player gets the initial selection screen again to restart the game-start process.)
When the game starts, you will see the “play” page:

The screen is divided into 5 parts
When you are tailing an enemy plane, play is no longer simultaneous. The plane being tailed must make their selection first. The tailing plane will have a “Please wait” screen.
After the plane being tailed has selected a maneuver, they have the “Please wait” screen while the tailing plane receives an indicator of the direction of the maneuver selected by the plane being tailed. In this example, the tailed plane has selected a “Straight” maneuver.
In this picture, you can also see the letter “T” showing up next to the blue plane, showing that the Allies plane is tailing the German plane. Also, you may be able to see in this picture the two small white circles on the wings of both planes, showing that each plane has taken 2 points of damage so far.
When you are actually being shot at, the background of the cockpit view will turn red, showing that you have been fired at. Additionally, a red circle will be shown around your plane on the overhead view:
In this example you can see that the Allies plane is directly behind the German plane and has done 4 points of damage to it.
You can see:
The game does handle the modified “hit table” for the Allies DH2. Here’s an example of a 1-point hit by the DH-2 on a German Eindecker E-3:

When both planes are in the same location, the enemy plane no longer appears in the cockpit view, and your view from the plane is indicating the direction that the enemy plane is headed.
You can see:
When both planes are facing forward, the enemy plane in the overhead view completely obscures your plane.

When the planes have flown too far away from each other, you will get this search screen:

When a dogfight ends, if there are more dogfights to be fought, both players are presented with a “Continue” or “Concede” page:

At the end of the game (either all dogfights have finished or a player has conceded), a final results page is shown along with providing a button to return to the lobby.

If you need to suspend a game, or if you lose your connection for any reason, you can use the “Reconnect to a game” menu option. It will bring up a page showing games in progress. Select the game you wish to continue and you will be reconnected to that game. (This works the same as with FBS)