Here are a few legendary Pokemon and how you get them. I sadly don't know how to get Groudon, Deyoxis, rayquaza, giratina or Kyogre.
Articuno Hatch a mystery egg in the upper left corner of the map (in the waterfall) (Articuno can hold or drop a frozen feather)
Zapdos Hatch a mystery egg in the lower left corner of the map (near the shop in the electric storm) ( Zapdos can hold or drop a power supply)
Moltress Hatch a mytery egg in the lower right corner of the map (where the fire is) (Moltress can hold or drop the flame of Moltress)
Lugia Get a Pokemon that has strength as ability (like Charizard). Make sure you get a frozen feather by killing Articuno (has 25% chance of dropping it). Use strength near the boulders in the water zone (close to a cave entrance). Enter the cave, and walk near the trees. The trees will disappear (so will your frozen feather) and walk further. You will see Lugia now. (Lugia can hold or drop a Lugia essence)
Ho-Oh Make sure you kill all three legendary birds (Articuno, Zapdos and Moltress) and get the flame of Moltress from Moltress. Then go to the middle right of the map, where the burning house is. You will be able to go in. Walk towards the door, and kill the second door that blocks the way (that one is vulnerable). Walk further, DO NOT GO INTO THE PORTAL! Go right, and you will see Ho-Oh. (Ho-Oh can hold or drop a Ho-Oh essence)
Celebi Kill the 2 trees in the grass area (at the top right of the map). For that, you should use a good psychic Pokemon. Then Celebi will come. (Celebi can hold or drop a strange egg)
Mew Get 3 mysterious eggs and 1 pokepouch (free capture is also handy). Go to the upper right of the map, where a cave entrance is with a door in front of it. Wait till it's night, then the door will disappear. Go as far into the cave entrance as you can, and use the 3 mysterious eggs. Then use the pokepouch. Mew will appear after a short while.
Mewtwo Make sure you get Mew, the Ho-oh essence and Lugia essence. Give Mew the 2 essences, and Mewtwo will appear. !WARNING! you will only be able to have 2 Pokemon because Mew will disappear!!! MAKE SURE YOU HAVE 1 OPEN POKEMON SLOT!
Manaphy Make sure you get 2 frozen feathers from Articuno. Also make sure you get the strange egg from Celebi. Go to the psychic Pokemon zone and go into the small puddle with those black things in it. The frozen feathers will disappear, and the egg will hatch into Manaphy. !WARNING! Manaphy will have a stats swap ability. It's very useful, but it will ruin the game for the people you swap stats with.
Power supply , for Zapdos.use the power supply near the power plant (windy area bottom left , in normal pokemon zone )
Flame of Moltres , for Moltres (obviously) use the flame of moltres on the lava with the 4 fire columns , bottom right (near the end of fire pokemon zone)
Icy feather : for Articuno , use the Icy Feather on the waterfall , top left of the map (near the end of the water pokemon zone )
Mew's tory : for Mew , use Mew's Toy in the night on the top right of the map , where is a gate which opens only at dusk.go there at dusk and use it.
Mew's Dna : for Mewtwo , use Mew's Dna at the top of the map , when you are close to the laboratory , mewtwo will come out..
With the artifacts of Johto:
Flaming dog whistle : for Entei (entei means flame emperor in japanese ) use the flaming dog whistle at the crater found at the top of the fire pokemon zone.
Wet dog whistle : for Suicune (this is also japanese, don't know what it means though , something with water) use the wet dog whistle at the obelisk found in the middle of water pokemon area
Charged dog whistle : for Raikou ( same goes for this ) use the charged dog whistle at the tip of the arrow in the electric pokemon area.the arrow is found right above the end of the map , noot right nor left , in the middle.
Silver feather : for lugia , go to the cave in the water pokemon area , reach the end , there's a different terrain , use it there.
Shiny rainbow feather : for Ho-Oh (this one's really powerful) go to the flaming tower on the right , turn left at the 2 turns , move ahead a bit , you'll find 2 fire torches , use it between them.
with the artifacts of Hoenn:
Ancient Tablet : for Regirock , Registeel , Regiice . between the psychic pokemon area and the grass pokemon area , there is a cave entrance of 4 rocks.go in there.you will find 3 circles of power.right is registeel , top is regirock , left is regiice choose a circle , step inside it and use the Ancient tablet..
Red orb : for Groudon , on the right side of the map , below the grass pokemon area and above the fire pokemon area , there is a cave blocked by rocks.break the rocks go in , move forward and you will find some lava terrain.use the red orb there
Blue orb : For Kyogre , this is the hardest one to get, below Lugia's cave , there is an entrance although it does not look like an entrance , just walk through the shallow waters and you will teleport somewhere else , there , go a bit far from the lever on the rocks , and left-click it . you will be transported across . next to another lever . then move on.you will find a watery area , like a pond , use the blue orb there.to go back , stand close to the lever and left-click it . you will be transported back where you came from.then just go back.
Meteor Fragment : for Deoxys , go next to the power plant* in the windy area and use the meteor fragment , deoxys will come (*read how to get zapdos to find where the power plant is)
With the artifacts of Sinnoh:
Most times these artifacts will drop other artifacts of other regions , but when they don't , they drop the items needed for the rarest legendaries inthe game.
Strange Egg : for Manaphy , go to the pond with the black spots , above the north poke-ball shop , get in the pond , and use the strange egg . manaphy will come
Dimensional distortion : for Giratina , go above the normal pokemon area and below the water pokemon area , there's a cave entrance. go in , don't enter the portal , head straight ahead and you will find a different terrain , use the Dimensional Disortion there .
Glowing molten rock : for Heatran , go to the cave in the fire area , left of the place where you can find Moltres . enter the cave , go right , use the glowing molten rock on the lava there . Heatran will spawn .
Shard of the New moon : for Darkrai , go bottom left , near to that tomb-like crypt (when you get close your pokemon will be put to sleep for awhile automatically , that's due to the presence of Darkrai.) get to the steps of that crypt and use Shard of the new moon . Darkrai will come .
Tribute to the gods : for Arceus (which is considered the god and creator of all Pokemon world , in this version though , i don't believe it lives up to it's name.although it's pretty good. )so , go to the big temple below the south poke-ball shop . enter the temple , go straight ahead , and you will find 6 or 7 portals the one next to the other . don't try to enter the portals , just stand infront of the middle one , and use the Tribute to the gods . Arceus will come..
Now the two specials :
Celebi and Regigigas
Celebi : Destroy the two trees raging in the grass pokemon area , celebi will come ,it's a tough one , so be careful .
Regigigas : Gather all 3 Regies (registeel , regiice , regirock ) and enter the cave found right of the waterfall in the water pokemon area . move ahead and you will find a big giant . the 3 regies will be turned into 1 , Regigigas . this guy is the best tank in the game , really something you can depend on to put first in the final battle .