After getting your first Gym badge, the Trio Badge, you can get the C-Gear from Fennel.
Where is Fennel's House?
You can find Fennel at her house in Striaton City. Fennel's house is the house directly to the south of Striaton Gym, which is in Striaton City.
When can I get the C-Gear?
After getting your first gym badge, you can get the C-Gear. Go to Fennel's house and go up the stairs to her lab. Talk to her and she will ask you to get some Dream Mist for her from the Dreamyard. She also gives you the HM for Cut. Teach it to a pokémon of your choosing, because you need to use Cut in order to get the C-Gear. Now head on over to the Dreamyard.
How do I get the Dream Mist?
Go to the Dreamyard. Use Cut to cut down the tree that blocks the opening to the Dreamyard. Once you head in, Bianca will arrive. You'll hear a strange sound, and then Munna will float over to you. Munna has the Dream Mist that Fennel needs.
But before you can get it, a couple of Team Plasma grunts arrive on the scene and start kicking Munna to try to make it give them the Dream Mist. Not good. When Bianca tells them to stop, they retaliate by threatening to "liberate" (in other words "steal") your pokémon.
You'll have to fight each of the grunts. They really aren't that tough.
After the fight, they'll leave you alone, but they'll continue kicking poor Munna. Suddenly, though, several copies of Ghetsis will appear and express annoyance with the grunts. Confused, the grunts will run off. Then Musharna will appear and rescue Munna. They will leave behind a pokéball containing the Dream Mist.
Giving the Dream Mist to Fennel
Suddenly Fennel will arrive. Bianca tries to explain what just happened, and Fennel understands. Fennel explains that Musharna can create dreams and was able to create a vision of Ghetsis to confuse the grunts into running away so that they would leave Munna alone. Fennel takes the Dream Mist and asks you to meet with her at her house.
At Fennel's house, you will receive the C-Gear. This device allows you to connect with other players. Read more about how to use the C-Gear.
Exploring the Dreamyard
If you haven't already, you should go to the Dreamyard and explore a little bit. You can occasionally find Munna in the grass, although it's not as common as Patrat and Purrloin at this location. There are also some items hidden around here.
Continuing on to Route 3
When you're ready, you can head west to the topiary garden, where some of the bushes are shaped like pokémon. There are people to talk to here, but no trainers that you can reach. You can walk up through the exit now that you have a gym badge (the person standing there doesn't let you through if you don't have a gym badge.) To the north is Route 3.