Pokemon Mystery Dungeon: Red Rescue Team

You have to beat the game, you have to get a gold to lucario rank, your level has to be high, you have to brought only one pokemon the size of the pokemon is 4 star .once they join the friend area is open

First beat the game. Now make sure you are a good level. The higher level the easier it is to recruit them. A friend bow also helps. Go into the dungeon with only one or two star size as the birds are four star size. Now get up there and beat them. They come with their own friend area. If they don't join the first time keep trying until they do.

First,beat the game.
Then,after the main storyline,go to the Dungeon of the specific Legendary.
The rescue rank you are doesn't matter.Get a high level pokemon (30-100) and attach a Friend Bow to them(not necessary but recommended for a bonus 10% of getting a Legendary)If there's a save point in a dungeon,good,save there and battle the Legendary.Defeat it and it maybe joins your team!If not,reset the game and go to your last save point and do it again.Eventually you will get them :)
Just got Groudon and Rayquaza,too :D

Once you beat the game, go back and fight them, and they will have a chance of joining your party, as long as you have at most a total of 2stars as your party size. Basically don't have more than 2 pokemon in your party.

Groudon and Rayquaza automatically give you their friend area if you recruit them.

The 3 birds have a 30% recruit rate if I recall correctly, and Groudon and Rayquaza have -10%, which means you need to either be above level 40 or have a friend bow equipped.

Alright first thing first get to a higher level like 45 is a good level because that is what level they are when recruited they are quite easy if you brought someone with ice beam for rayquaza just make sure YOU get the final blow.