So first, you gotta go to Monstro Town and rest at the Inn. Then, you'll find Azelf at the end of Bandit Way, Mesprit in Tadpole Pond where Toadofsky used to be, and Uxie at the "Left Left Straight Right" screen of the Forest Maze. Then, you can find them in their hideyholes, in the last pipe of the Ice Cave, down the pipe in Mushroom Way, and the tiny nook in Booster Pass.
After that, Dialga and Palkia can be found at the beanstalk path (the alternate route where you can find the Hyper Wrist), Giratina can be found at the secret entrance in Nimbus Land where the Fertilizer used to be, and Arceus can be found in the last screen of the castle, the one where Mario plummeted through clouds.
Kyogre's at the last screen of the Sea in the newly-made entrance down below, Groudon's in the Barrel Volcano, and Rayquaza is found upon revisiting Bowser's Keep and defeating Magikoopa, where jumping on the spring will take you where you need to go.
Then, Latias and Latios will appear in the Random Encounters that enemies like Tonberries or Amazy Dayzees hide. The trick is to get into an encounter, then run away, stay in the same spot, and repeat until Latias and Latios show up.
Then there's Celebi, which can be found the earliest, but is the hardest one to catch (use the Master Ball on it, unless you want a challenge). If you go to Nimbus Land and buy the Dream Cushion, you might see a dream with Celebi with it where a three-digit number between 000 and 255 will appear, with a question asking if you'd like to accelerate time (which boosts the number by a certain amount, I forget what amount it is; surpassing 255 takes it back to 000, so be careful). In the Forest Maze, if the number is 255, then Celebi appears, but the number will only increase if you use the above method, enter a place with a random encounter, or get into a random encounter. Thus, your best bet is to raise the number to around 250 using the methods above, use a savestate, go to the screen before the Maze part of Forest Maze, alternate between the screens four times since the random encounter Brachiosaur is there (254), then get into a random encounter (255), and you should see it.