When you enter the Snagem Hideout, you will get an E-mail invitation for Realgam Tower, you can head there now if you like. Regardless, head inside the building to begin. And just to note, there are no Shadow Pokémon here, so relax.
There are nine trainers and a boss inside, so you should gather supplies beforehand. As soon as you enter you have to battle a trainer that's weak to Psychic and Flying type moves. Afterwards, check out the healing machine on the right; you can heal your Pokémon here at any time. Take the North stairs to the second floor. Head south on the second floor and battle Jedo, who has four poison type Pokémon with him. Go north-east after the battle to reach some more stairs; take them, and head south. You will come across TM29, which teaches Psychic. Pick it up and take the stairs next to it after battling Biden.
Biden has a couple of Poison types with him, so you may want to use that TM you found if you lack a good Psychic move right now.
After the battle you may want to return to the Healing machine because the Boss is up those stairs. When you're ready, go up.
Ah, another trainer before you get to the boss. Fire, Electric, and Bug or Dark should take care of his team.
OK, now for the Boss; Team Snagem Leader Gonzap! Gonzap has three Pokémon weak to Fire, so keep any fire users you have alive. He also has a Whiscash; Grass type moves will take it down, but make sure to knock it out quickly; it can destroy fire types very easily. His other Pokémon is Electrode. Hit it hard with any ground type moves to beat it, and have a ground type out, even i it doesn't know any ground type moves; Ground types are immune to electric attacks.
If you win (He is hard, so explore the rest of the base if you aren't strong enough yet) you will get the Snag Machine back. If you look aaround the room you will get Gonzap's key, which opens the locked treasure chest deeper in the hideout, which contains the TM for Shadow Ball. When you're ready, leave for the Cipher Key Lair.