I've only tried this out as a two player game, but here's how it works. Each player sets up their countries as normal (include a neutral as well). Deal the deck into three piles and have each player pick one (the unpicked is the neutral). Place one guy on each country/area you draw. Then take turns placing the rest of the neutral and your guys as you normally would. When this is done each of you shuffle your country pile and pick one at random. Place a horse on this space, as well as a flag miniature (or something that could represent a flag). This is your base. Keep the country card you drew as your flag's base. Now play out a normal game of Risk with the objective being to capture the enemy flag and get it back to your base. This is how it works:

When you reach a space marked as the enemy's base, if you overtake the base, all of your guys moved to that space are now in control of the flag, and will only lose it to the enemy if they all die and the enemy takes control of that space again. To move the flag back to your home base, you must send at least one guy from that country to another country. He takes the flag with him and that becomes the new country guarding the flag. You may only move the flag location when you end your turn and move the infantry from one space to another, or when the infantry on that country take over another touching country.

Winning: You win if you make it back to your base with the enemy flag. However you must still be in control of your flag and it must still be at your base to win. If the enemy has it or you have it on a different space, you must retrieve it.

If both players start off with bases really close to each other you may consider either choosing again or choosing the base.