First and foremost, lets start with the Pokémon:
Smeargle is a great all-round Pokémon, as it's the only one that learns Sketch. It will learn Sketch every 10 levels starting from level 1, meaning by level 31 it will have 4 moves. Sketch will permanently copy a move used in battle, meaning that Smeargle can learn almost any move.
You can guarantee the move Smeargle gets when using Sketch by entering double battles such as the ones in Restaurant Le Nah. Send out both Smeargle and the Pokemon whos move you want to copy, get it to use the move you want, such as False Swipe, and using Sketch, 'attack' your partner.
So how do I build the ultimate Pokémon Catcher using Smeargle?
With 100% accuracy, Spore is the preferred sleep move, but it is a little harder to get access to in X & Y.
Foongus learns it at level 50 (Amoongus at 62). Otherwise you can get a Paras through Friend Safari or GTS, who will learn it at 22. Shroomish will learn it at level 45.
Nevertheless Sleep Powder is the other safe option. Butterfree will learn it on level 12. Nice and easy. Otherwise Hoppip/Skiploom on 16 and Oddish/Gloom on 17.
I listed Stun Spore as a tertiary option, as some people swear by Stun for catching. Again Butterfree on level 12, Hoppip/Skiploom on 14, or Oddish/Gloom on 16 are your best bets.
False Swipe should be fairly obvious. It will bring a Pokémon down to 1HP, and never kill it. Perfect for catching Pokémon. As it's a Normal move, Smeargle also gains a Same Type Attack Bonus (STAB) when using it, bringing it's power from 40 to 60 (or from 60 to 90 with the Technician ability, see below).
It's TM 54, which can be found in Professor Sycamore's Lab. Talk to a woman on the third floor - she will give it to you. Teach it to any of these Pokémon.
Otherwise, Scyther can be rarely found on Route 21 and will learn it at level 13. your other options are Axew, Karrablast, Cubone or Zangoose (levels 24,25,27 and 29 respectively).
Taunt / Ingrain / Mean Look
This slot is a little up to personal preference.
- Taunt will force a Pokemon to use offensive-only attacks, meaning they won't be Teleporting/Roaring/Whirlwinding or inflicting status (at least from pure status moves). However it only lasts 2-4 turns.
- Ingrain will prevent Roar/Whirlwind/Dragon Tail/Circle Throw from making Smeargle flee, and also restore a little health at the end of a turn. However it doesn't stop Teleporting, and it means that Smeargle cannot be switched out.
- Mean Look prevents the target from switching out or fleeing (including via Teleport). Useful for Pokémon such as Abra, however unlike earlier games there aren't a lot of Pokemon that flee on sight.
As for the ease of getting these moves:
- Croagunk will learn Taunt on level 10, or Absol on level 17. Taunt is also, TM 12, and can be found in the back of Team Flare Cafe. Talk to the Team Flare guy in the room with the beds you can sleep and heal in. Here is a video showing the path to take (minor spoiler).
- Ingrain is learned by Foongus on level 18, Phantump/Trevenant will learn it on level 13, Snover/Abomasnow on level 31 and Ferroseed/Ferrothorn on level 35. There are others, but these are probably the easiest to get a hold of.
- Gastly learns Mean look at level 8. You could try taking a Haunter to the move relearner for the cost of a Heart Scale, or you could throw a female Haunter into daycare with a male Haunter or Litwick. You'll have a wee baby Gastly in no time. Other options are Jynx on level 25, or Zubat on level 34.
Soak is awesome. I'm sure some people who were reading about False Swipe and Mean Look were crying out "But they don't work on Ghost!"/"False Swipe isn't very effective against Rock!". Well I'm here to tell you. Soak changes the target Pokémon's type to Water.
Not only does this mean that False Swipe/Mean Look will hit Ghost (and Rock/Steel normally), but Spore/Sleep Powder can hit soaked Grass-types too.
And as an added bonus (man I sound like a salesman), the enemy Pokémon no longer gets STAB from it's typed moves (meaning Smeargle takes less damage).
However, getting access to it may be a little harder. Psyduck will learn it on level 36 and is probably your best bet. At the time, I threw a Psyduck in daycare, put on the TV, and rode in a circle around the Eiffel Tower in Lumiose (Side note: good to know for breeding). Otherwise GTS is your best bet.
Ok, that's a good start, but what about Natures/Items/Abilities/IVs/EVs?
Lucky Egg can be used for an XP boost whilst levelling up. Find it in the Hotel in Coumarine City (talk to a girl there).
Metronome can be used to boost the power of consecutive False swipes (10% each turn). Again, head to Coumarine City, and check the Monorail station.
Some people also recommend Silk Scarf, for the immediate 20% boost to False Swipe it brings. If you're running the Technician ability (see below) you should probably go with Metronome. Can you guess where Silk Scarf is? That's right, COUMARINE CITY. Talk to the old man in the house by the docks.
Own Tempo or Technician (Player's choice)
This comes down to personal preference. Own Tempo will prevent confusion (which can be useful), whereas Technician will boost False Swipes power by 1.5x (from 40 to 60) (Which is then again boosted by STAB)
It's hidden Ability is Moody, but I don't think it's useful in this situation. Stick with Own Tempo or Technician.
Completely optional, but Jolly (-SpAtk, + Speed) or Adamant (-SpAtk, +Attack) are probably the best ones. Honestly you'll get away with anything though.
Come on, you're facing off against wild Pokémon, it doesn't really matter. If you feel like trying to beat your best times in Super Training, avoid Special Attack. Everything else is personal preference. I spread mine over Speed, Attack and HP, in that order.
Don't even bother.
- Do note that Smeargle won't attempt to learn Sketch if it still already knows Sketch, so make sure you use it before leveling up!
- Pokemon with the abilities Vital Spirit, Insomnia or Overcoat cannot fall asleep, and therefore will stop Spore.
- Soak can be countered by Pokemon with Magic Coat/Magic Bounce.
- Soak also wont help Spore land on Grass Pokemon with Sap Sipper, and will be negated entirely by the abilities Storm Drain, Water Absorb or Dry Skin. some Pokemon that can have these abilities are Maractus, Lileep, Cacnea/Cacturne & Paras/Parasect.
- However As listed by Trent below, having another Pokemon with Gastro Acid/Simple Beam/Entrainment or Skill Swap would be a good counter to Pokemon with these abilities