Catch it in route 116
You can catch Skitty in Pokemon Omega Ruby and Alpha Sapphire in the barks of trees.
Route 116
You can get a Shiny Skitty in a 1 in 1800 chance that a shiny Pokemon will appear, let alone the odds of having a Skitty Swarm appear on route 116.
With a PokeBall. It is rare, so try to lower its HP as much as possible.
you can't catch it in any version
The only way I know is to look behind the Pokemon Mansion or to migrate one from Ruby, Sapphire, or Emerald.
Skitty can be found on route 222 by sunnyshore city on a certain day because they are swarm pokemon. In ruby and sapphire they can be found on route 116 at a 2% chance.
Yes, Pokemon Sapphire version is the version in which you can catch Latias. You can only find it once you have beaten the Pokemon League, then there is a report of a legendary red flying Pokemon in Hoenn. Latias appears randomly.
No, Skitty is not in that generation.
Sadly, you can't catch Groundon is the Sapphire Version, however you can in the Ruby version, you will find him in the same place you find Kyorge in the sapphire version.
You can't: you can only get it in a trade from a person with either Pokemon sapphire version or emerald version.
jump on a bike and eat its tail