Continue east from Route 220. Fight the male Swimmer, and continue east until you reach land. Head east on the northern section Route 221, stopping at the Level House (see below) to pick up the Pure Incense which allows you to produce a Chingling Egg when breeding Chimecho. When you reach the Pal Park (inaccessible until after you defeat the Elite Four), head back along the southern part of the route, collecting all the items you missed when travelling on the northern part. Now that you're finished here, it's time to Fly back to Jubilife City and head northwest via Route 218 to reach Canalave City.
The only house located on Route 221 belongs to an old man who will each ask for a Pokémon at a certain random level from 1 to 100 each day. The items he'll give you are the Black Belt, Expert Belt, or Focus Sash. Only one item is given to you out of that particular order when you complete his request, and after he gives you the Focus Sash, the cycle will start over.
For days where the requirement is an extremely high-leveled Pokémon, there isn't much you can do. On some days you might get lucky and be able to use Pokémon from your regular team. For days where low-level Pokémon are needed, the quickest solution is to simply head to an earlier area with an Ultra Ball or two, catch a Pokémon of the appropriate level (if you don't have one in storage already), and bring it to him.
Now that you have Surf, you're able to navigate the rest of Route 218 and reach Canalave City, your next destination. There isn't much to do on this short route except for fighting the Trainers and catch Mr. Mime (this is the only location in Sinnoh where they can be found).
When you enter the guard post separating Route 218 from Canalave City, Professor Rowan's assistant will approach and give you upgrade to your Pokédex. This will allow you to check the differences in appearance between the same Pokémon in their Pokédex entry, such as gender or form differences.
When you first enter Canalave City, be sure to visit the Pokémon Center to heal and prepare your team - when you try to cross the bridge your rival Barry will show up and challenge you to test your skills.
Barry now has a Heracross on his team, but a powerful Flying-type move can easily beat it. Unless you have an especially fast one, avoid using Psychic-type-types as Heracross's Dark-type move Night Slash will counter it. Four members of Barry's team have reached their highest evolutionary form, but they shouldn't be too much of a problem as long as your party is at least at Level 35 and has good type coverage. After the battle, Barry will rant a bit (as usual) before heading off towards the library.
The Move Deleter resides in the house just north of the Poké Mart. He will be able to remove any unwanted moves in your Pokémon's present moveset including HM moves. This is the only way for a Pokémon to forget a HM.
The southernmost house on the west side of town belongs to a Sailor named Eldritch, who handles the ferry in town. Nothing important will happen here until the post-game after obtaining the National Pokédex. Eldritch is waiting near his boat at the dock nearby, and he can take you to Iron Island. South from the wharf is a hidden area where you can pick up the TM89 (U-turn).
Canalave Gym 1F
Canalave Gym 2F
Canalave Gym 3F
Canalave Gym 4F
Be aware that the toughest Pokémon you'll face here is Level 41. The layout of the Canalave Gym is a maze consisting of multiple elevator platforms. As you may already know, it specializes in Steel-types. You'll want Fire-, Ground-, and/or Fighting-type Pokémon with you. Steel-types resist attacks of almost every other type, and are completely immune to Poison-type moves. Also, most of the Pokémon in this Gym have high Defense, so Special moves will do the most damage to them. Lucario's Aura Sphere is one of the most dangerous moves to Steel-type Pokémon in the game right now.
To deal with the maze, first head to the easternmost elevator out of the set of four you'll find on 1F. Then, take the elevator south of you on 2F to reach the southeast area of 1F. The next one will take you back up to 2F. Then, use the moving lift hooked up to a wire to get across the ledge. Take the regular elevator there to reach 3F, where you will find more moving lifts to take you across the wires. First, use the moving lift north of you to reach the north area of 3F with two moving lifts side-by side. Take the northern lift and then keep following the path that will take you back down to 2F. Another elevator will take you to the northern area of the 1F. There, an elevator with a red outline will take you up to 4F where Byron, the Gym Leader and the father of Oreburgh City Gym Leader Roark is.
Byron starts by sending out Magneton, whose weak Sp. Defense makes it vulnerable to moves like Flamethrower. Also, a Ground-type move like Earthquake could easily take it out in one hit due to its Steel/Electric typing. Beware of Flash Cannon if your Earthquake user is part Rock-type. Metal Sound will harshly lower your Pokémon's Special Defense, causing Thunderbolt, Tri Attack, and Flash Cannon to do even more damage, so be careful. It's best to use Special attacks on Byron's Steelix because of its high Defense stat. It will dispose of Fire-types with Earthquake unless you have a Fire-type strong and fast enough to take it out in one hit. Ground Pokémon, on the other hand, must watch out for Ice Fang. Don't worry too much about Steelix's Flash Cannon, as its Special Attack isn't the best. The last Pokémon you'll face is Bastiodon, which is high-leveled but can easily be defeated by a powerful Fighting- or Ground-type attack due to it's type combo of Rock/Steel. Be sure to take it out in one hit (which isn't too hard), or your Pokémon will be on the receiving end of Metal Burst, which does 1.5 times the damage your previous attack did to Bastiodon. Stone Edge poses a threat to Fire-types, and Iron Defense will sharply raise Bastiodon's already high Defense stat. Taunt will only allow your Pokémon to use attacking moves, which shouldn't be much of a concern. Get Bastiodon out of your way as quickly as possible, and you'll have saved your team some pain and earned yourself the Mine Badge without too much trouble!
Once you defeat Byron, he will give you the Mine Badge, which causes all traded Pokémon up to Level 70 obey you without question and allows for Strength to be used outside of battle. He'll also give you TM91 (Flash Cannon), a Steel-type Special attack that occasionally lowers the enemy's Special Defense stat.
When you step out the door, your rival Barry will be there waiting for you. After congratulating you on getting the Mine Badge he asks you to come with him to the Canalave Library. Meet him there, then head in the building and go up to the 3F. It turns out that Professor Rowan is there with his assistant Lucas/Dawn and wanted you to be part of this conversation. Rowan explains that during his exploration of Pokémon evolution, he learned of the Lake guardians that might shed some light on the mystery of evolution he is trying to solve. He is therefore going to investigate the lakes where these three guardians live, and while he is going with his assistant to Lake Verity, you will go to Lake Valor, and Barry is going to Lake Acuity. Just then a tremor goes off, and you'll learn there was an explosion at Lake Valor, and so the group then separates to head to each of their destinations. You can go to yours immediately, but some extra training at Iron Island, as your rival suggests, may be helpful. Additionally, since you now have six badges and can use Strength, you can backtrack for items you couldn't get before in places such as the basement at Oreburgh Gate.
At the entrance to the mine you'll meet a man named Riley, who will give you HM04 (Strength). He mentions he is training inside and proposes you join him. While receiving the HM is the only required part of your mission here, you'll find some good items, get valuable training, and an extremely rare Pokémon if you explore the whole mine.
In the west side of B1F there are just two items and a single Trainer. One of these items is the Protector which can evolve Rhydon into Rhyperior if it is held while traded. Afterwards, return to 1F and this time use the right-hand stairs to reach the east side of B1F.
On the right-hand side of B1F, you will again face one Trainer and find some more items, including another hidden Star Piece. Make sure to keep an eye on your bearings here since it is easy to get lost in this maze. You need to stay on the correct path to find the items and get to the small elevator that will take you down to B2F. Once again, there are two pathways. Since Riley can be found by taking the left stairs, let's go right first so afterwards Riley can heal your team.
In B2F's east side you will face two Trainers, and also find TM23 (Iron Tail). If you follow the path that leads to the other side of where the TM was found and use your Dowsing Machine, you will find yet another hidden Star Piece.
Once you reach the left side of B2F, Riley will team up with you to investigate the mystery of a disturbance here in the mine. Just like Cheryl and Mira, he will heal your team after every battle, and double battles will also occur in the wild. Therefore, you should train as much as possible while he is with you.
Remember, like all Multi Battle situations, two wild Pokémon will appear at once and you can't catch a wild Pokémon unless you knock the other out. Since the Trainers in this room are positioned to where you could face them in a Double Battle, do not waste the opportunity to do so, if you wish.
Just like B1F's east room, B2F's west room is also a maze so make sure to get your bearings for collecting items or facing Trainers. Your final target is the pair of Galactic Grunts in the south area of the room - be warned, Riley will leave after you face them. After defeating Workers Brendon and Quentin head southwest and follow the path to reach a ledge above them and then use the Dowsing Machine to find a fourth hidden Star Piece. Also in the southeastern area down some small stairs, the Dowsing Machine will reveal a hidden item, the Iron Plate.
After getting past the somewhat tricky Ace Trainer duo Jonah and Brenda, you'll find the Galactic Grunts - the disturbance in the cave.
After you defeat the grunts, Riley will thank you for your help and will give you a Pokémon Egg containing Riolu, Lucario's pre-evolution. As long as you remembered to only bring five Pokémon with you, there should be no problem; if not, you'll have to return to Canalave City first to empty a slot in your team and then backtrack to get the Egg.
All that's left is taking the elevator down and entering the final room.
Use the elevator here to go back up to ground level and you'll find the Shiny Stone, for evolving Togetic into Togekiss or Roselia into Roserade. Since you can only get one of these the regular way, you'll have to raise a Pokémon that has Pickup as far as Level 41 to have a chance of getting another Shiny Stone.
Also, you'll find the entrance to the Iron Ruins, which will become a shrine to Registeel if you have an eventRegigigas. If not, it will be an empty room where you can find a Metal Coat. Even if you do have the event Regigigas, you won't be able to face Registeel until you have the National Pokédex.
Leave Iron Island and return to Canalave City so you can have your Gym battle. If you have time, you could hatch the Egg and raise Riolu's happiness factor to evolve it since Lucario will be of great use in the next two Gym battles, especially since it learns Aura Sphere at Level 37. Just remember, Riolu only evolves during the daytime once its happiness factor has been raised high enough.