there are three types of legendary pokemon
 ones that are found in one spot and moving legendarys and those only obtainable through
event gameshark or AR

the first type is entei raikuo sucine
the second is mewtwo articuno moltres zapdos 
the third Deoxys mew lugia HO-OH

the first type is easy to catch  
articuno is in the seaform islands ( alot of work required strenght and surf needed)
moltres isle one mt ember(little work required Strenght and surf needed)
zapdos powerplant( less work required surf needed)
mewtwo cerulean cave(ALOT of work required strenght and surf required but rocksmash may
also be a good thing to have)

first step to catching them is to go to those places and find the once you see them dont
just jump into battle svae the game first so if u fail u can restart ur gameboy and start
over then weaken the enemy until low yellow hp or red hp red is better then try to paralze
or make the opponet sleep ten throw ULTRballs at them until caught

The second type is hard u can only catch one depending on your starter 
grass starter= fire entei
water starter= electric Raikou
fire starter = water /ice sucine
after you have the nat dex you can find them anywhere(not on islands) becareful you dont
know where they are until u find them. you might need an arena trap pkmn or mean look
knowing pkmn so they dont escape. then weaken them red or low yellow and either paralze
them or put them to sleep. then use your Ultra balls

the third type can be obtained from events AR or GS
after that you can find  MEW LUGIA HO-OH DEOXYS 
mew i think plays a game with you ( not sure) then it is equivalent to the first lugia
Ho-oH on same isle and they are equivalent to the first type of legendary
deoxys is a puzzle you must push a stone until it turns red then it appears and is
equvialent to the first type of legendary pkmn
and thats how to catch a legendary