When you step out of Skyla's Gym, N will come up to you. He will talk to your pokémon to find out more about you. Maybe he can really talk to pokémon, or maybe he's just making it up. After all, I'm sure that he could have his Team Plasma people do a background check on you to find out all of the things that he said. But maybe he's for real?
Anyway, he'll say that Team Plasma is looking for the Light Stone and Dark Stone, which contain the essences of Reshiram and Zekrom. His plan is to revive a legendary Dragon pokémon and befriend it, then separate all pokémon from their trainers in order to protect the pokémon. He does say that he can tell that you and your pokémon have a trusting relationship, and he says that he'll be sad to separate you. If all pokémon and trainers had such trusting relationships, he would be satisfied with the current state of the world and would leave pokémon and trainers alone.
N will walk away, so you can continue on your journey.
Finishing Route 7
In case you didn't fight the two Harlequins east of the house on Route 7 where you can heal up, now is the time.
Harlequin Pat has an L30 Emolga and Sigilyph. Use Ice or Rock moves on Emolga. For Sigilyph, use a Dark pokémon and attack with Dark moves.
Harlequin Pat has an L29 Tynamo, Ducklett, and Tranquill. For Tynamo, use a Ground pokémon with Ground moves. For Ducklett, use Electric moves. For Tranquill, use Electric, Rock, or Ice. A Steel type pokémon with Electric moves is a good choice.
Near the entrance to Twist Mountain, there is a hidden Ultra Ball, so be sure to use your Dowsing Machine after fighting the last Harlequin.
Battling Cheren outside of Twist Mountain
As you approach the stairs up to Twist Mountain, Cheren will appear and challenge you to a battle.
Cheren's pokémon are an L33 Liepard that knows Assurance, Torment, Fake Out, and Hone Claws, an L33 evolved elemental monkey that is the same type as your starter (Simisage, Simipour, or Simisear) that knows Lick, Leer, Fury Swipes, and a strong Elemental move of its type. Simisage knows Seed Bomb, Simipour knows Scald, and Simisear knows Flame Burst. Cheren also has an L33 Unfezant that knows Roost, Detect, Air Slash, and Taunt, and his L35 starter (Servine, Dewott, or Pignite). His Liepard holds a Sitrus Berry, his monkey holds an item that boosts its elemental move, his Unfezant has a Scope Lens (increases critical hit frequency) and his starter has Leftovers.
For the Liepard, a good opponent is Scraggy. Its Dark type protects it from Liepard's Dark moves, and Fighting moves are super-effective against Dark pokémon.
For the monkey, if it's Simisear, try using Tirtouga or Boldore. If it's Simipour, try using Deerling or any Grass type. If it's Simisage, try using Tranquill.
For Unfezant, try using Emolga, Klink, Archen, Boldore, Excadrill, Zebstrika, Tynamo, or Tirtouga.
Finally, for the starter, if it's Servine, use Litwick and attack with Fire. If it's Dewott, use Foongus and attack with Grass. If it's Pignite, use Palpitoad or Boldore.
After you defeat Cheren, Alder will compliment you on the battle, and he'll hop down from the ledge and give both of you HM03 Surf.
Surfing for Pokémon and items
Now that you have Surf, you can teach it to a pokémon and go around catching pokémon that you couldn't get before. These are: Basculin, Frillish, Alomomola, and Jellicent (which is the evolved form of Frillish). Frillish has a different form for male and female, as does Jellicent. Alomomola can only be found in bubbling spots on the water.
You can also go to Route 1 and Surf to Route 17, which leads to P2 Laboratory and Route 18. There are some good items there, such as the HM for Waterfall, and an egg containing a Larvesta.
You can also explore more of Wellspring Cave and find some trainers and items there. You will need Flash for the basement of Wellspring Cave.
Legendary Pokémon that you can catch after receiving Surf
Once you have a pokémon that knows Surf, you can catch Cobalion and Virizion.
Pokémon that you can catch in Twist Mountain
In Twist Mountain, you can catch Boldore, Woobat, and Gurdurr. In Winter, you are likely to encounter Cubchoo. However, in other seasons, Cubchoo is less likely to appear. Also, a rare type that you might encounter here is Cryogonal. It's extremely rare in any season, but is slightly more likely to appear in Winter. Swirling dust will be Drilbur.
Just outside of the entrance to Twist Mountain, you find Hiker Terrell, who has an L34 Boldore and Gurdurr. For Boldore, Frillish is a good choice of an opponent for its immunity to Normal attacks. You could also go with Ferroseed, which is strong against Normal and Rock moves, and will have super-effective Steel moves. For Gurdurr, any of the pure Psychic types will be a good opponent: Munna, Gothita, Solosis, and Elgyem.
Inside, you find Hiker Darrell, who has an L33 Woobat, Gurdurr, and Boldore. For Woobat, try using Liepard, Zoroark, or Krokorok.
Next, you will encounter Ace Trainer Carol, who has an L35 Vanillish, Gothorita, and Duosion. I recommend using Klink against Vanillish. For Gothorita, I recommend using Scraggy, Ferroseed, or Klink. For Duosion, Scraggy and Krokorok could be good opponents, as could Excadrill.
Next, you find Battle Girl Sharon, who has an L36 Throh. I recommend using Woobat or Sigilyph.
Next you find Worker Brand, who has an L34 Boldore and Excadrill. As before, use Frillish or Ferroseed against Boldore. Frillish is also my recommendation against Excadrill. Palpitoad could be used as a backup against Excadrill.
Worker Heath has an L35 Swoobat. Against it, you can try Liepard, Zoroark, or Krokorok. Klink could work as a backup.
Worker Rob has three L33 Boldores. Frillish or Ferroseed are good opponents for them.
Worker Cairn has an L35 Excadrill. Try using Frillish, with Palpitoad as a backup.
Doctor Hank has an L34 Duosion and Musharna. Against Duosion, try using Scraggy, Krokorok, or Excadrill. For Musharna, any Dark type will be immune to Musharna's attacks, and their Dark moves will be super-effective, so go for Scraggy, Krokorok, Liepard, or Zoroark as the opponent.
After this you meet Hiker Neil who has an L34 Woobat and Boldore. As before, use Liepard, Zoroark, or Krokorok, and for Boldore, use Frillish or Ferroseed.
Next is Black Belt Teppei with an L36 Sawk. As with Throh, try using Woobat or Sigilyph.
Finally you encounter Worker Rich who has an L34 Gurdurr and Boldore Try using Munna, Gothita, Solosis, or Elgyem against Gurdurr, and try using Frillish or Ferroseed against Boldore.