To use a scenario, simply copy it into the scenario directory in your AoE folder. Campaigns belong into the campaign directory.
To play the scenario, choose "Single player, scenario", for a campaign, select "Single player, campaign" in the game.
Fun scenarios are scenarios that do not follow the usual concept of building up a civilization, but work in a different way. You will find arena-like scenarios there.
When playing multi player scenarios, make sure that all players have exactly the same (latest) version of the scenario, or you cannot start the game. Kali supports automatical updates - it will copy the offered scenario to the right position.