Although you’ve been tasked with finding the Seven Sages of Team Plasma, you only need to find six of them to complete your mission, as Ghetsis’s location remains a mystery.
Each Sage will give you a TM for your trouble, and only a few need you to fight any enemies, making it a fairly simple task.
Sage 1: Rood
He’s standing at the end of Route 18. To reach him, Surf from the beginning of Route 1, across Route 17, and then follow Route 18 all the way to the western point to find the sage staring mournfully out to sea.
Gives TM32 Double Team.
Sage 2: Gorm
Head to the Dreamyard, north east of Striaton City. To the top right, there are some stairs leading underground where you’ll find trainers with Level 60+ Pokémon. Make your way to the bottom right of this room and head up outside, he’s to the south waiting to ambush you from the trees.
Gives TM75 Sword Dance.
Sage 3: Ryoku
Head to the bottom level of the Relic Castle. During the story, this is where you found Alder and were automatically taken outside, but this time, you can continue through the door to the right. You’ll have to fight one Plasma Grunt on the way and be close to a rare Pokémon.
Gives TM04 Calm Mind.
Sage 4: Bronius
Enter Chargestone Cave from its northern entrance (via Icirrus City) and take the stairs down two levels, traveling as south as you can in this room. Two Plasma Grunts with Level 60 Pokémon will attack you efore you can secure this sage.
Gives TM69 Rock Polish.
Sage 5: Zinzolin
Hiding in Cold Storage, where you found Team Plasma hiding during the course of the story.
Gives TM01 Hone Claws.
Sage 6: Giallo
You’ll need to get HM05 Waterfall for this (you can find it near Sage 1). Simply head onto Route 14, southern entrance preferably, and ride the waterfall upstream.
Gives TM08 Bulk Up.