Pokémon XD: Gale of Darkness/Cipher Lab
The Cipher Lab has a lot of battles and a lot of Shadow Pokémon, so head back to town for supplies if you run low on stuff. Before you can enter the building, however, you must battle at least one of the Hexagon brothers. They each have a Shadow Pokémon, so battle them all if you want to get the Shadow Pokémon now instead of later.
 Finding Professor Crane
The door on the right only has a couple of items in it, so grab them and take the door on the left, which has a heal machine and a PC. Then take the elevator in the back, but be prepared for an ambush...
Head east after you get out of the elevator to reach an another elevator to take. This one drops you off even lower into the Lab. Battle the people you come across, grab the Peon's Shadow Spinarak, open the chest for a Revive, and take the stairs.
Go south after climbing the stairs and, after the cutscene, continue further south to battle a guy with a Shadow Numel. After the battle you'll reach another elevator, take it.
After you get off the elevator, there is another elevator next to you that takes you to a healing machine and an Elixir, but it will be guarded by a trainer without Shadow Pokémon. Afterwards, go left, down, left to reach the next elevator; explore the rest of the floor for more items.
Exiting the elevator, you reach a room with more ambushes, first with a Peon carrying a Shadow Carvanha. Keep moving straight ahead to avoid another Peon without a Shadow Pokémon, but you'll miss out on the Full Heal. At the end of the hall you'll reach a room with scientists talking to each other; you know the drill. Don't leave without examining the table, it has an ID Card on it, which is needed to reach Prof. Crane.
Take the north exit to the room and battle the Peon that ambushes you. Take the elevator that follows by using your new ID Card on it.
Keep moving after going through the elevator to find Professor Crane and another Peon. Beat the Shadow Pokémon-free trainer and bring the Prof. back to the top of the Lab after saving first.
When you reach the elevator that you used to enter the lab with at the beginning, you will be stopped by Cipher Admin Lovrina, who won't let you leave without a battle.
 Cipher Admin Lovrina
Lovrina has four Pokémon; Luvdisk, Beautifly, Roselia, and a Shadow Delcatty. Use Fire or Flying on Beautifly and Roselia, and use whatever Pokémon you have that are the same gender as her other two since they use Attract. Work her down to just having Delcatty and try to capture it. If you don't, remember that you can get any missed Shadow Pokémon back later on.
After the Admin Battle, grab the Data ROM that she drops and return to the Pokémon HQ. The Purify Chamber is ready for use now, so either take in the in-game lessons on it or read the Purification Chamber page. Go talk to Datan, who is outside, and he will tell you to bring the Data ROM to Pyrite Town, your next destination.