After you have selected the 6 Pokémon you want to transfer in the menu before loading your game, go to the Pal Park in Route 221 and they will give you the Park Balls. Now these balls have a 100% capture rate and once you find your Pokémon, you cannot even run so you have to capture it. And thus you go in
There are many areas to find the Pokémon in, with the Pokémon going into the certain area that fit with the Pokémon. For example Sea Pokémon going into the small sea area in the Park
There is also a Pond area for the Pokémon to be found in, aswell as a Mountain Side. However just being there does not consittute as you finding the Pokémon. Some Pokémon can be very very rare and hard to find
And there is the usual Grass areas that a lot of the Pokémon will be found in. Both Short Grass and Tall Grass and they're all around the park
When you meet the Pokémon, they have the exact same stats, level, moveset, Effort Values and keep whether its Shiny and keeps its Original Trainer and location. Just throw the Park Ball and its yours. It IS the exact same Pokémon as you had on your old game so do not worry
If you managed to capture all of your Pokémon within a certain time constraint, you will be congratulated and the Pal Park Ranger will give you a special Berry

Want to see what Pokémon is where? Select the area below:

Field Area | Forest Area | Mountain Area | Pond Area | Ocean Area