You'll get this achievement during episode 4, you just have to examine the following items (in the listed order) which make out the "numbers" from the TV show;
• 4: On the right side of the beach is a small hut with a suitcase covered in stickers
• 8: On the right side of the beach near the ocean someone has arranged some shells into a figure 8.
• 15: On the left side of the beach is a hut, the side of is made up by a part of the plane.
• 16: On the left side of the beach is a crate underneath a cover.
• 23: On the beach to the side of Hurley.
• 42: On the beach Charlie is sat near a table, examine the domino box.
Once you've examined all of these items you'll be presented with an option to fast travel to the medical station, once you're there the logo is on the wall at the bottom of the stairs. When you're done just fast travel home.
Below is a video which shows you what to do, follow it and you'll get the achievement.
Credit to elemen7s for the video