The Trio of Birds.
The three birds named Articuno, Zapdos, and Moltres are all on an island called Orange Island. To get there you must go to Tm. Draken which is in Drakebreath City and fight Lance. Once you defeat him, he will give you the orange pass which you will use on Bramboch town to get a airplane ride there. Make sure that you choose the storm place for these guys because the field place is for another pokemon. You will swim to the West and then North for Zapdos, North for Articuno and East then North for Moltres.
Mewtwo & Mew.
To get to Mewtwo you simply have to go to Drakebreath City and swim up to Team Steam's base and when you are in there building be sure to go through the door on the left and then just walk up the stairs. After you either capture Mewtwo, kill him or run away leave the building and fly to Serenity City and run West into the route there and look for Mew. He will be above the bit of water you first see but not on or in the water.
The Sacred Dogs.
The three legendary dogs are Suicune, Entei and Raikou. They are usually in the same route as everyone else for the first time after you defeat Eusine in Kosoka city. First to get to Raikou you must fly to Rocavely City and if you go a tad North there is a cave called Mt. Lauren and if you just through the cave and then over the rock (need rock climb) he should be sitting right there. For Suicune you need to go to Ironnem City and go north. You will swim on the left side and it will be on a mini island. For the last dog Entei fly to Flamerny City and run West a tad and run into Flamerny Forest. If you run to the right side and North you will see Entei in about 3 seconds. A little hint is they can use roar and will end up in an unknown location. The only other location I can give you if Entei runs away is at Mt. Vulcan.
Lugia & Ho-oh.
Once again in Kasaka City after you already defeated Eusine he will have given you a rainbow pass which will be used for the Ho-oh and for Lugia you will need both Eusine beat and Lance because to get to Lugia you need the orange ticket which you obtain from Lance back at Tm. Draken in DrakeBreath City. First for Lugia you will want to go to Bramboch Town and take the airplane to the field location and once you get there go South East and use dive on the nearest dark spot of water. Once you get down there you will need rock climb to get to the bottom and then eventually though the place you will see Lugia. For Ho-oh you need to go to Noormeak City and take the air balloon on the right side. Once you get there just follow the mountain until you find him.
The four I'm talking about are Regirock, Regice, Registeel and Regigigas. For the first three Regie's you will need to have defeated Steven in Snowce City. For Regirock, fly to Gorment city and run West into the cave Mt. Shuem. For Registeel fly to Gorment City and run North East into Mt. Zhery. For Regice fly to Snowce City and run South into cave Mt. Icestorm. For Regigigas you will need to have beat Shinora in Noormeak City. Next go to Suner town and swim to South until you get to the beginning of the World Championships. Then go through the cave near the bottom left of the first island there. RUnning through the cave will get you to him.
Groudon, Kyogre & Rayquaza.
Groudon, Kyorgre and Rayquaza are all found after beating Steven in Snowce City. For Groudon go to Seanport City and swim out east and the North a tad and East again and you will be in Imartari Island and then you will see a small mountain and it's called Mt. Origen and you will find him pretty quicky there. To get Kyogre go to the same Island area but near Mt. Origen you will see a dark part of water. Dive into it and look through the small cave to find it. For Rayquaza go to Ironnem City and look for Mt.Sky which should be right near the city. It's an easy path to the top to find him.
Jirachi & Deoxys.
For both of them you need to defeat Steven from Snowce City. Deoxys is located in Ironnem City and is basically right behind the pokemon center. Just look a tad North and you will see him. For Jirachi you have to go back to Yellow Town and talk to Ash who is standing South East of where you start when you fly there. Then go to the world championship and swim East and then a bit North and he will be on a little island called Wish Island.
Darkrai & Cresselia.
For both of them you must defeat Shinora in Noormeak City. For Cresselia go to Merydian City and sleep in a bed and you will be teleported to the distortion world and she will be right there. Do the same thing for Darkrai but sleep in a bed in Darkdust City.
Manaphy, Heatran & Giratina.
For Manaphy & Heatran you must defeat Shinora in Noormeak City. For Manaphy go to Zhery Road and run South. Once you do swim until you see a dark patch of water and go down it. It will be waiting right down there. For Heatran go to Mt. Vulcan which is in Flamerny City. Just run through the whole cave and Heatran will be at the end of it. Giratina is not needed to kill people this far or to even beat the league but is fought in the distribution world during game play.
Dialga, Palkia & Arceus.
For Dialga & Palhia you must defeat Shinora in Noormeak City. Go to Tm. Oren from Snowce City and on instead of going right through the middle of the mountain go to each side and click on the signs and they will teleport you to them. The right side is Palkia and the left side is Dialga. To get to Arceus all you need to do is beat both leagues and then go to to Noormeak city and go in the balloon on the left which will take you to Alpha Island. Just go to the top of the mountain and he will be there.
Zekrom, Reshiram & Kyurem.
For Zekrom & Reshiram you need to defeat Blane in Carmin Town and then go to Mt. Winter where they will both be on different sides of the mountain. To get to Kyurem you need to defeat Blane and then fly to Drakebreath City. Once you get there run north and then swim north until you see the land that isn't the victory road. There will be a long path to follow and he will be at the end of it.
Shaymin & Celebi.
For Shaymin you need to defeat Blane in Carmin town and then run into Inhore Woods. Once you get in just run and look around in it. For Celebi you have to defeat Eusine in Kosaka City and then fly to Darkdust Woods and then run West in there and he will be there.
Latias & Latios.
For both of them you need to have beat Steven in Snowce City. For Latios you need to go to Bromboch City and run East and go into the water. It will be there. Latias can be found if you go to Emery Town and run West into the water.
Alzelf, Uxie, Mespirt.
You need to defeat Shinora in Noormeak City for all of them. For Mespirt she will be South of Darkdusk City.
Virizion, Kobaruon & Tekakion.
You have to defeat Blane in Carmin Town for all of them. Virizion can be found just by entering Inhore woods. Tekakion is found from going South into the grass from Marydian.
The Pokemon that I did not catch but wonder around the game:
Alzelf & Uxie: Beat Shinora.
Kobaruon & Terakion: Beat Blane.
If I do end up finding them I will edit this post later on.