I still see a great deal of misunderstanding and misinformation floating around about this quest. This post will hopefully save players some aggravation, frustration, and long periods of unnecessary waiting.
Procedure
1) Baggin's Birthday starts with an Auto-Bestowal quest directing you to speak with Frodo Baggins in Rivendell. Take the quest.
2) Travel to Rivendell and speak with Frodo Baggins, located inside the Last Homely House, first floor, right side, behind a door near the Vault Keeper. He will ask you to speak with Gaffer Gamgee in Hobbiton.
3) If you have no quick path back to Rivendell, consider taking the Milestone just down the road from the Last Homely House in Rivendell.
4) Travel to Hobbiton and speak with Gaffer Gamgee. He is located across the river, on The Hill, below the Party Tree. He will give you a list of story tellers and ask you to read it. Click on the story list next to the quest. Now speak with Gaffer Gamgee again. He will direct you to speak to Ted Sandyman.
5) Travel back toward the river and speak with Ted Sandyman, next to the Mill. He will give you a quest. Talk to him again to hear his tale and complete the quest. This will bestow a deed to collect 12 tales related to the disappearance of Bilbo Baggins, of which you now have one. You may now speak with active storytellers as described below.
6) Speak to 11 hobbit storytellers and collect their tales concerning the disappearance of Bilbo Baggins. Four storytellers reside inside the Ivy Bush, five reside in Hobbiton near the tavern, and two reside on The Hill, above the Party Tree.
6a) At the top of every hour, server time, exactly 4 of 11 hobbit storytellers, chosen at random, will become active. (Ted Sandyman, the 12th hobbit storyteller, always tells his tale at step (4).) These four hobbit storytellers will remain active for the next hour and display a quest ring for that period. The other 7 hobbit storytellers remain inactive for that hour and do not display quest rings.
6b) Speak twice to any active hobbit storyteller available to you, once to take his or her quest and once to collect his or her tale and complete the quest. A character may only collect each tale once. This means that if you previously collected the tale of an active storyteller, he or she will not show a quest ring or speak with you. As a result, you may see three, two, one, or zero active storytellers in a given hour, depending on your progress collecting tales.
6c) After collecting tales available that hour, you may leave Hobbiton. The server will not select a new set of active storytellers until the top of the next hour.
6d) Return to Hobbiton each hour and collect tales from active storytellers. You need not come every hour. Obviously, the more often you come back and check, the better your chances of quickly collecting all 12 tales.
7) After collecting all 12 hobbit tales concerning the fate of Bilbo Baggins, you will complete the story deed and automatically advance the main quest. Speak with Gaffer Gamgee, located across the river, on The Hill, below the Party Tree. This will complete the main quest and award the final birthday quest, to take the collected tales to Bilbo Baggins in Rivendell.
8) Travel to Rivendell and speak with Bilbo Baggins, located inside the Last Homely House, first floor, beyond a door on the left side. Bilbo will talk about the tales presented, then show a quest ring. Speak with him one last time to complete the final quest in the birthday sequence and earn a bookstand (small furniture) for your efforts.
Hobbits and Locations
Ted Sandyman...................... .Across the river from Hobbiton, in front of the Mill
Sheriff Robin Smallburrow......Inside the Ivy Bush tavern
Dudo Chubbs........................ .Hobbiton, next to the Task Board
Lobellia Sackville-Baggins.......The Hill, above the Party Tree
The Storyteller................... ....Inside the Ivy Bush tavern
Hal Hornblower.................... ..Hobbiton, next to the Stable
Bogo Cubb.......................... ...Hobbiton, next to the Stable
Lotho Sackville-Baggins..........The Hill, above the Party Tree (Also Brockenborings, inside the Plough and Stars tavern)
A hobbit child......................... Inside the Ivy Bush tavern
Hereward Loamsdown.............Inside the Ivy Bush tavern
Holly Hornblower.................... Hobbiton, behind the Ivy Bush tavern
Postman Grubb.......................Ho bbiton, at the Post Office
Strategies
1) If you have multiple characters, run each one through steps (1) through (5) above, then position them in Hobbiton. At the top of each hour, sign onto each character in turn and collect any new stories. Keeping a spreadsheet detailing who collected what stories speeds up this process. After cycling through all your characters in a given hour, go do something else. When a given character collects all 12 tales, advance him or her to step (7).
2) If you have one character, run him or her through steps (1) through (6) above. You have now collected 5 of 12 tales. Note the hour. Grab the milestone in Hobbiton. Go do something else. Return to Hobbiton about 55 minutes into the NEXT hour and collect any new stories. Wait for the hour to pass then collect stories again. Now go do something else for about two hours. Repeat until you have all 12 tales, then advance to step (7) above.
Example:
7:26pm: Run to Rivendell and get quest.
7:31pm: Arrive in Hobbiton, speak with Gaffer Gamgee, Ted Sandyman, and 4 active hobbit storytellers. (5 of 12 done)
7:40pm to 8:54pm: Do something besides standing around in Hobbiton.
8:55pm: Return to Hobbiton and speak to active storytellers. Collect three more stories. Wait. (8 of 12)
9:01pm: Speak to active storytellers and collect one more story. (9 of 12)
9:05pm to 10:54pm: Do something besides standing around in Hobbiton.
10:55pm: Return to Hobbiton and speak to active storytellers. No new stories. Wait. (9 of 12)
11:01pm: Speak to active storytellers and collect two more stories. (11 of 12)
So on...
FAQ
1) How many hobbit storytellers become active each hour? Exactly 4. If you see three, two, one, or no active storytellers, you already collected a tale from each missing hobbit.
2) Is there any pattern to the storytellers? Based on personal experience with 13 characters and data from other players, the server chooses storytellers at random.
3) Will new storytellers become active at half past the hour? No.
4) If I stand next to the hobbit I need and wait, will it help? Based on personal experience with 13 characters and data from other players, no.
5) Do the quests in this chain award Bounder's Bags? Yes. Every character completing the entire Baggin's Birthday quest chain will earn approximately 15 Bounder's Bags.
6) Can Free to Play and Premium players complete the Baggin's Birthday quest chain and reach Rivendell? Yes. You may ride overland to Rivendell on your personal horse, use slow stable mounts (South Bree to Forsaken Inn to Ost Guruth to Rivendell; requires previous discovery of all stables on route), use a Mithril Coin to Swift Travel from South Bree to Rivendell, have a Captain summon you to Rivendell, or have a hunter take you to Rivendell.
7) Can I have your stuff? No.
I take full responsibility for any errors or omissions in this post. If you find an error or omission, please write up the issue and I will ammend this post as necessary.
Edit (9/22/13; 3:58pm): Added list of hobbits and locations, FAQ question 5, and FAQ question 6.