Battle Moveset

A Good Moveset for Delcatty would have to be this:

Attacks:

Heal Bell
Toxic
Charm
Return

Items Attached:

Leftovers

Preferred Nature:

Timid

Strategy Using Delcatty

For a fully evolved pokemon, Delcatty has been given poor stats and it can't really do much other than to provide some annoyance.
Delcatty's ability allows for a built in attract affect, so that gets rid of the need to use attract. Toxic is to poison your opponent and providing more annoyance.
Heal bell is useful if your opponent has the Synchronise ability or tries to use status effects on you. Return gains something from STAB and is there just for an attacking move.
There isn't much else that Delcatty could do, you could try it as a baton passer, but I doubt it would survive enough turns to gain the boosted stats and then pass them onto a new pokemon.
Other than poor stats, there isn't anything else to explain about Delcatty, its a shame really that such a cool looking pokemon would be given such poor stats.

EV Corner:

Max out the EVs in Defense & HP for Delcatty with any remaining in Special Defense

Strategy Against Delcatty

Delcatty's Defenses are both below average, however it's Special Defense is lower than it's Physical. So attack with a volley of Special Attacks or Fighting Type Attacks

Contest Moveset

A good Contest Moveset for Delcatty would have to be this for the Cute Contest best with Timid, Hasty, Jolly or Naive Nature:

Attacks:

Bulk Up
Rock Smash
Earthquake
Rock Slide

Items Attached:

Pink Scarf

Strategy Using Delcatty

If you do the attacks in this following order you should have very few problems; 1st - Bulk up, 2nd - Rock smash, 3rd - Bulk up, 4th - Rock smash, 5th - Earthquake/Rockslide

Locations in Games

Ruby/Sapphire Evolve Skitty Colosseum Trade from R/S Fire Red/Leaf Green Trade from R/S

Animé Appearences

Delcatty has had a few of Anime Appearences. First, Butch and Cassidy were sent to kidnap a trainer in Cerulean's Delcatty and with Misty and Casey's help, Team Rocket were beaten and the Delcatty kept by the trainer. After that, May met a Co-ordinator who had one and used it in her Contests Special 12: The Seriousness of Misty's Match! Risking A Life! Episode 336: Skitty & Delcatty! Enter the Legendary Co-ordinator!