Unlocking

• The first 20 entries of the A Realm Reborn Sightseeing log are unlocked by completing a level 20 quest A Sight to Behold, available from Naoh Gamduhla at the Carline Canopy (11-13) in New Gridania. The next 60 entries of the A Realm Reborn log are unlocked upon speaking with Millith Ironheart at the Apkallu Falls (10-6) in Old Gridania after finishing the first 20 entries.
• Heavensward Sightseeing logs are unlocked by talking to Kester Ironheart in Tailfeather and completing Sights of the North.
• Stormblood Sightseeing logs are unlocked by talking to Ulger Ironheart in Rhalgr's Reach and completing Sights of Crimson and Dawn.
• Shadowbringers Sightseeing logs are unlocked by talking to Eirlalth (9.5-9.7) in The Crystarium and completing Travelers of Norvrandt.
• Endwalker Sightseeing logs are unlocked by talking to Babeth Ironheart (13.4-16.9) in Old Sharlayan (Zone) and completing Sights of the End.
• Dawntrail Sightseeing logs are unlocked by talking to Elsebee Ironheart (14-10.2)) in Tuliyollal and completing Sights of the West.

Completion

In order to complete an entry, you must find the specific location being hinted at and perform a specific emote.

A Realm Reborn's logs also require a specific time of day under specific weather with the right emote. You will know when you have found the right spot when the message "You have arrived at a Vista." appears in your chat log. If you move too far away from that spot, the message "You have strayed too far from the Vista." will appear and you'll need to move back so the first message appears again. If you perform the emote at the wrong time of day or in the wrong weather, or if you perform the wrong emote, nothing will happen. If you do the right emote at the right time and under the right conditions, you will be surrounded in a nimbus of light and a large message in gold letters, along with a small picture of the location from your Log Book, will appear on your screen.

The latter Sightseeing Log entries are a lot more lenient. There is a glowing blue orb of light showing you the spot where the Vista is (the ARR log locations are invisible, hence the reason for the Vista message.) You also only need to be at the location (standing on that blue orb of light) and perform the right emote in order to unlock that Log entry; there is no time of day or weather requirement, save for entries 48 and 58 in the Stormblood log.

Rewards

• Completing the 1-20 entries in the A Realm Reborn Log will reward you with the Out of Sight achievement, and completing the entire A Realm Reborn log will earn you with the Out of Sight Out of Mind achievement, which in turn rewards you with the Fledgling Apkallu minion when you 'Share a tale' with Jonathas (in Old Gridania at Apkallu Falls.)
• Completing the 1-42 entries in the Heavensward Log will reward you with the Out of Sight Out of Bounds I achievement, and completing entries 43-62 will give you Out of Sight Out of Bounds II.
• Completing the 1-45 entries in the Stormblood Log will reward you with the Oh, the Sights We'll See I achievement, and completing entries 46-62 will give you Oh, the Sights We'll See II.
• Completing the 1-45 entries in the Shadowbringers Log will reward you with the Darksighters I achievement.
• Completing the 1-46 entries in the Endwalkers Log will reward you with the End in Sight achievement.
• Completing the 1-45 entries in the Dawntrail Log will reward you with the Happy Trails achievement.