Catch Legendary Pokémon Easily

Have a legendary you want to catch? This article can help!

Steps

Catch a Sneasel/Scyther, evolve it into a Weavile/Scizor and teach it False Swipe. False Swipe does decent damage for a 40PP move, but always leaves the Pokémon with 1HP.
Catch a Gastly and teach it Hypnosis. Hypnosis sends the Pokémon to sleep, making it incapable of attack and easier to catch. (Although Pokémon roaming around the map may still flee.)
- If you are planning to catch a roaming Pokémon (Mesprit, Latias, etc.) teach Gastly Mean Look, which prevents wild Pokémon from escaping.
Level up your Pokémon as high as you can.
Buy as many Ultra Balls as you can. (Although some Pokémon may be better caught with others. Case in point, Groudon is the heaviest Pokémon ever so will be most vulnerable to Heavy balls.)
Go find that Legendary!
Engage the Pokémon in battle and use False Swipe to whittle down it's HP and use Hypnosis to send it to sleep.
Keep throwing Ultra Balls (or whatever you have) until the Pokémon is yours.

A good Pokémon to catch Roamers is Crobat, who evolves from Golbat with friendship. He can't learn False Swipe, but can learn Hypnosis and Mean Look. Also, it's incredibly fast.
Sneasel can be caught at Routes 216 and 217 and the Snowpoint Temple in Diamond, Pearl or Platinum and Mt. Silver in Heartgold and SoulSilver.
The Grip Claw can be found in Route 224, Victory Road and Cyrus's room in Team Galactic HQ in D/P/Pt and can be bought at the Battle Frontier for 48BP in all 4th generation games.
Sneasel can evolve into Weavile if it levels up holding the Razor Claw at night.
Gastly can be caught in Route 209 and the Old Chateau in D/P/Pt and in the Sprout Tower in HG/SS.
Gastly will evolve into Haunter at level level 25 and Haunter become Gengar when Traded.

Legendary Pokémon have a reputation of breaking out of Pokeballs even after being sent to sleep and having their HP reduced to 1.
48BP is a lot in the Battle Frontier, so for HG/SS, it's going to be a while.
This advice is solely for the DS games, but it can be implied to some extent in older and newer games. (Just remember, Sneasel won't evolve in the older games and has weaker moves.)
Hypnosis is inaccurate, so you may have problems.
Save before fighting the Pokémon for if you kill it, it will never show up again.
Roaming Pokémon will retain any damage and Status conditions inflicted on them during the battle if they flee. Remember that.
Bring Healing for your own Pokémon, just in case.
Pokémon that are put to sleep can wake up so putting it to sleep multiple times during the battle will be necessary to prevent you from taking lots of attacks.