As you will quickly figure out, this Gym specializes in Water-types. Grass- and Electric-types will do well here, but you shouldn't use Fire-, Rock-, or Ground-types. The strongest Pokémon here is level 37, so make sure your team is leveled appropriately before challenging the Gym.
The puzzle of the Pastoria Gym may appear complicated at first, having to raise and lower the water level by stepping on buttons in the correct order. In reality, there is only ever a single path that you can take at any one time without going back the way you came. To reach Crasher Wake (the Gym Leader), go down the entrance stairs, turn left and go up those stairs. You will reach a yellow button. Hit it and the water level drops. Turn right, down the stairs, and go through a narrow passage. There is another narrow passage before you reach some stairs. Climb up to the top, and hit the green button. Climb down and follow the path to another set of stairs. Battle the Sailor there, and hit the blue button. Follow the platform to the first yellow button and head right, past the stairs to the Tuber. Battle him, and follow the path right to another Tuber. Battle her, and go on forward. You will eventually find a green button. Hit it, go down the nearby stairs, and hit the yellow button. Go up, then down to the lowest level. The rest is simple; follow the path to a set of stairs, climb up, and hit the blue button. The path to Wake is clear.
Wake leads the fight with Gyarados, who has Intimidate, so lead with Special-based attackers. It knows Wake's signature move, Brine. Brine does more damage if its target has less than half of its HP left, so be wary and keep your Pokémon healthy. Waterfall will do the most damage and may cause your Pokémon to Flinch. However, one good Electric-type attack, such as Spark or Thunder, will take it out. Next up is Wake's Quagsire, whose Ground type makes it immune to Electric-type moves. Grass-type attacks are this Pokémon's nightmare, particularly Special attacks due to its weak Special Defense. It has Rock Tomb which can slow you down, but it doesn't know Brine. Yawn can be annoying, because a Pokémon hit by it will fall asleep on the next turn unless you switch it out. Chesto Berries as held items can be useful in this situation. Last up is his star Pokémon, Floatzel. Floatzel is very fast, and can hit pretty hard, but its defenses are quite low. It has Ice Fang to counter Grass-types, as well as Aqua Jet, a Water-type version of Quick Attack. It too is packing Brine, so stay healthy during the fight. A Pokémon with a good Electric move will do well here.
After defeating Wake, you'll receive the Fen Badge that lets you use Surf outside of battle, as well as TM55 (Brine).
After earning the Fen Badge, you'll meet up with Barry again. When Wake leaves the Gym, it turns out that Barry's earlier claim that he's Wake's apprentice isn't true - Wake won't take him on as he believes neither of you need any tutoring. After this exchange Barry mentions a Galactic Grunt with a bomb near the Great Marsh's Observatory Gate. When you meet Barry and Wake at the entrance to the Great Marsh you'll find that the Grunt sets off a small bomb in the Great Marsh as a field test, and you'll have to chase after him while Barry keeps people out of the Great Marsh until Wake can be sure it is safe.
Go down the stairs and around the path past the Scientist and the two Rangers. Head up another set of stairs to grab TM62 (Silver Wind) across the narrow bridge. Go north on the wide bridge, Cut your way through some bushes, and collect all the items hidden on the four hills connected by the three narrow log bridges. East of the wide bridge is the house of one of the three Move Tutors who offers to tutor moves in exchange for shards.
Trek through the three large sections of mud, using your Dowsing Machine to find a number of items hidden in the mud along the way. Make a detour to the north underneath the first narrow wooden bridge to collect the item at the end of this dead end path,
then cut your way through the small trees you just passed and use your bicycle to cross the bridge. Battle your way past the two trainers and find a Zinc where the path ends in a ledge. Make another detour into the muddy area north of the signpost to find a Dawn Stone hidden in the mud, then continue west.
Unless another player can trade you a Manaphy, you need to visit Route 212 in order to obtain the National Pokédex. After leaving Hearthome City, head south to the entrance of the Pokémon Mansion. Once you're done visiting the mansion, cut your way through to find a path leading to TM11 (Sunny Day). Follow the shoreline of the pond next to the grass to reach the other half of this route.
The Pokémon Mansion is owned by Mr. Backlot. It is also the home of the famous Trophy Garden, which is located at its rear. It has four rooms, the most important of them being Mr. Backlot's office, which is where a Pokémon statue guarded by a policeman is located. The guard is on break from 2 A.M. until 6 A.M., leaving you free to touch the statue and get your fingerprints all over it. Manaphy's data can be recorded (as a seen Pokémon) from the book lying on Mr. Backlot's desk, and it must be done in order to get the National Pokédex. Other rooms in the mansion have beds, which you can use to rest yourself along with your Pokémon. In the west wing, you may fight the maids in the 5-Maid Knockout Exact-Turn Attack Challenge, in which five maids must be beaten in a certain number of total turns (no more, no less). The prize for beating the challenge is a duel with either Lady Celeste or Rich Boy Liam, depending on how many turns you were told to beat the maids in.
The western and eastern exits of the mansion are blocked by the maids. Neither of these doorways are functional however, and for your purposes serve only as decoration.
After speaking to Crasher Wake at the entrance to the Great Marsh, the grunt will try to run away. Head to Route 213 (you'll encounter Looker there), chasing the Grunt east towards Valor Lakefront. After talking to the man in the hotel lobby and healing up, chase the Grunt all the way to the Valor Lakefront, where he'll finally give up and you can challenge him to a battle near the entrance of Lake Valor. After defeating the Grunt, you will meet Cynthia and your rival again. He briefly interrupts her to report that the damage to the Great Marsh is not as serious as expected, and Cynthia states that she is worried about the group of Psyduck on Route 210. She gives you SecretPotion to cure them of their headaches, and will then tell you the legend about a mirage Pokémon that lives inside the lake.