Walk into Lumiose City after beating the Elite Four and upgrading the Mega Ring to begin this particular quest. You'll get an anonymous call on the Holo Caster telling you to go to the Looker Bureau in Rouge Plaza. You can take a cab there (select Facilities). Otherwise, it is in the alley directly opposite the Route 14 gate on North Boulevard.
Within, you'll meet Looker: you'll be well familiar with this guy if you played Pokémon Platinum. Opt to partner with him and we can continue the storyline. Speak with him after the initial conversation to be given a task: you need to find the five Looker Tickets distributed throughout the expanse of Lumiose City.
As you leave the bureau, you'll be given the locations of the tickets rather directly. ... How's that supposed to test us?
Ticket 1: Centrico Plaza
In Prism Tower (the Gym). We'll cover this one first since it's the easiest: if you look around the Lumiose skyline, you should be able to see the tower. Enter and you'll see a sparkle in the southwest corner: it's a ticket!
Ticket 2: Magenta Plaza
This one is within the Pokémon Center. Magenta Plaza is the northwest plaza of the city, but it's kinda hard to find from the Prism Tower as there are no specific landmarks there and the camera rotates annoyingly (okay, not quite annoying). So, guess and check, I suppose?
It's the same plaza where you can find the Lysandre Café at least. The sparkle within denoting the ticket is hard to see due to a lack of contrast, but it's in the northwestern part of the area - if you approach the changing room, you'll see it.
Ticket 3: Vernal Avenue
This one is in the Herboriste shop on Vernal Avenue. Vernal Avenue is the southernmost one of the city; if you go clockwise from the Route 4 entrance, or just outright use a cab, or leave the Pokémon Gym's inner area heading south then continue south, you'll reach it.
The shop in question is the second on the left when heading northward, the sparkle being easily spotted in the east-central area next to the table.
Ticket 4: North Boulevard (A)
This one is in the art museum on North Boulevard. If you look clockwise from the Pokémon Center here, you'll see a large white building across the street: that's the museum. Upon entrance, go due east and, next to the woman on the couch, will be the sparkle denoting another ticket.
Ticket 5: North Boulevard (B)
This one is in the hotel on North Boulevard, specifically Hotel Richissime. If you went to the art museum first, continue clockwise down the street: it'll be the next enterable building, a black one with a sign out front. To find the ticket, go to the far east into the corner, then go north: you'll see the sparkling thingy.
After finding all the tickets, return to the Looker Bureau - again, accessible by cab or in the alley opposite Route 14. Accept his request and we'll be finally allowed to open up more and more.