After you go north from Mauville City, you find an impassable desert with sandstorm. Go west from there to Route 112.
In this route, you can catch Numel. In Ruby and Sapphire you can catch Machop, and in Emerald you can catch Marill.
Explore the Route
As you go west, you see a grass area. South of it, there is Camper Larry, who has a Zigzagoon and Nuzleaf.
West of the grass area, there is Picnicker Carol, who has a Taillow and Lombre.
Go north up the stairs. Hiker Trent is up here. He has four Geodudes.
A little farther north, there is Hiker Brice, who has a Numel and Machop.
There is a cable car to the northeast, but there are Team Aqua/Magma Grunts blocking the way, so go west and enter the cave to go into Fiery Path.
Fiery Path Pokémon
In this cave, you can find Machop, Grimer, Koffing, Slugma, Numel, and Torkoal.
Go Through the Path
Just go north through the cave. Don't worry about the little puffs of smoke. They don't hurt you or anything. You will pass by a big rock on the left. You will be able to push it with Strength, but not until after you get the next gym badge.
After you go through Fiery Path, you come back out in Route 112. Go north and get the Rawst Berries and Pecha Berries.
Go east and you will be back in Route 111. Now you are north of the desert. You will find Cooltrainer Wilton, who has an Electrike, Wailmer, and Makuhita.
North of that, talk to the person looking at the tree. He gives you TM43 Secret Power. You can create a secret base by using Secret Power in front of special trees like the one that the kid was looking at, or in front of rock walls that have indents in them.
East of there, you can use Cut to reach the Old Lady's Rest Stop. You can also go north and east and south to get to the house. Go in and talk to the old lady to heal your pokémon.
To the north, there is a slope that you can ride up with the Mach Bike.
Talk to the girl nearby to get a free berry. You can collect the berries from the trees to the north.
To the west, there is Cooltrainer Brooke, who has Wingull, Numel, and Roselia.
West of there, you reach Route 113.