Alright, since no one's directly answered the main question, or has only briefly explained how, I'll step up and do so.
Entei, Raikou, and Suicune are found roaming the mainland of Kanto upon beating the Elite four and obtaining the national dex. They do not walk on water. Not even Suicune. They will not be found in the Safari Zone either. This limits you to roughly 15 places the beasts can be found at any given time. The best way to do so, as mentioned a few times, is to take a Pokemon roughly level 45 in level, and abuse Max Repel until it is found. Do not spend very long on a route. If the beast is supposed to be on that route, it will be found within the first three battles. Flying deters the beast, Suicune and Entei in your case, so limit your transportation to walking and biking. Flying farther away from the spot of the beats may "trick" it into moving towards you. Your Master Ball is the only guarantee when it comes to capturing it. If you cannot use the Master Ball for whatever reason, here are some tips on how to catch it:
- Sleep is your ally here. It won't prevent running, but it does make capture easier, and will linger after the beast flees
- Chipping away at the beast will allow you to steadily lower its health and bring it to the desired capture range
- The ability Arena Trap, carried by Diglet, Dugtrio, and Trapinch, will definitely assist the capture of the beast
- Each beast knows the move Roar, and if they use it, due to a glitch in every copy of FireRed and LeafGreen, known as the Roaming Roar Glitch, the beast will never be seen again. This means that the move Taunt will come in handy, preventing it from permanently fleeing
Finding Entei and Suicune, in your case, and to anyone searching for them, is stricly based upon luck. The "tricks" you've searched for on "sources" like WikiAnswers are fake, and do not actually work. That's just the luck of that one individual that caused events to transpire the way they did. Good luck and happy hunting.