Instructions
Find the Luck Bobblehead in the Arlington Cemetery. To get there, head into the Flooded Metro, located southwest of the Anchorage Memorial. Follow the tunnels and exit up the stairs into Arlington Cemetery. Find the Arlington House in the center of the cemetery and go to the basement. The Luck Bobblehead there will permanently increase your Luck by one point when taken.
Get the Lucky 8 Ball item. Head to Big Town, located to the north of Vault 101. Enter the clinic and talk to the nurse to hear that she cannot heal one of her patients, named Timebomb. If your Medicine ability is at least 40, talk to Timebomb and choose to heal him. As a reward, you get the Lucky 8 Ball, which adds one point to your Luck while held.
Find the Reilly's Rangers compound near Seward Square. Either kill one of the Rangers, or do a quest with them and wait for one to get killed by monsters. Take the Ranger Battle Armor from the corpse's body and equip it for one Luck point.
Get the Naughty Nightwear by exploring Marigold Metro Station, located next to Grayditch. The Naughty Nightwear gives you one Luck point when worn.
Take the Lucky Shades from the head of a mannequin in Lucky's Store. The store is found to the southwest of Tenpenny Tower. The Lucky Shades give you one extra Luck point.
Choose the Intense Training perk when you level up. This lets you add one more point to any S.P.E.C.I.A.L stat. Select Luck to get the extra point.