Randomly from a mob, you'll find a "Friendship Crystal". All you have to do is get some friends, talk to the elder, talk to another npc, get some exp and sp, rinse and repeat. I'll elaborate more on steps.

You and all friends must be level 30+, otherwise it will not work. So get leveling!

Step 1: Get a Friendship Crystal from a mob. Yay! Alternatively, you can be a friend to someone with a crystal. (Keep reading, it'll all make sense, hopefully)

Step 2: Get two friends WHO HAVE NOT LEAD A FRIENDSHIP QUEST ALREADY TODAY and go to the elder. Make sure you're the party leader and your two friends are standing next to the elder.

Step 3: Go to "Quest Related" for the elder and select "Have they been here before?" There will be a 2nd option saying "Trade in Memory Orb" which you should not select. MAKE SURE YOU CHOOSE THE RIGHT OPTION!!! Selecting the wrong one will result in an immediate 5k exp/1k sp and ending the chain. The elder should take your crystal (or Memory Orb) and you should receive a quest.

Step 4: The quest says to talk to the elder, so do it. Take the "True Friends" quest. The elder shoulud tell you to search for the "Girl in White".

Step 5: Fly to the southwest tower in the center of Arch (538, 643). Talk to the lady. She should say something along the lines of "Who are you! I don't need friends! Go away!" or something like that. You should receive a Flawed Pendant of Friendship. Your two friends should each receive a Memory Orb.

Most people stop here as the leader gets 15000Xp already. Read on only if you want the extra bonus 5000Xp.
Step 6: Here's where it gets confusing. What you need to do now, is have your two friends, which I shall call B and C, get two new friends each: D and E, and F and G. B and C should each be the leader of two separate parties. They should repeat the exact steps of 3-5.
Step 7: After friends B and C complete their trips with their two friends, they should receive a Flawed Pendant of Friendship AND a Stone of Friendship each. They should BOTH trade the Stone of Friendship to you. You should now have 2 Stones of Friendship and a Flawed Pendant of Friendship. (Note, Friends D, E, F and G can all repeat steps 2-5 as this is a chain quest that can go on forever)

Step 8: Fly back to the elder. He should have a quest for you to repair the necklace using the 2 stones. Do the quest, you should receive a Necklace of Friendship.
*NOTE: Some people have received 5 rep from the elder at this point in addition to the 5 rep you get next step. So far it seems random and very rare. If you get it, lucky you!

Step 9: Fly back to the "Girl in White" and talk to her. Give her the necklace and your done!

It should be as follow after completing everything:
20k exp
4k sp
5 rep
Tablet of Friendship (Called "Token of Friendship" in this game - it looks like an fb tab)
*Note: These are the rewards after you turn in the full pendant to the elder. This means, friends B and C can achieve these awards if they complete the whole chain, too.*

You can give the Tablet to the Girl in White for 5k exp, 5k sp and 5 rep. Alternatively, you can save up and get lv90 equips (see below).
*NOTE: You sometimes don't receive the 5k sp for some reason.
Prizes (Thanks Ence - see post 7)
All equipments are level 90 requirements and require 50 Tablet of Friendships
Heavy Arm Guards:
P.Def: +627
M.Def: +270
Str: +5-6
Dex: +5-6
Defense Level: +2

Light Arm Guards
P.Def: +269
M.Def: 420
Str: +5-6
Dex: +5-6
Defense Level: +2

Arcane Arm Guards
P.Def: +70
M.Def: +625
Dex: +5-6
Int: +5-6
Defense Level: +2

Heavy Boots
P.Def: +835
M.Def: +360
Str: +5-6
Dex: +5-6
Defense Level: +2

Light Boots
P.Def: +358
M.Def: +555
Str: +5-6
Dex: +5-6
Defense Level: +2

Arcane Boots
P.Def: +93
M.Def: + 835
Dex: +5-6
Int: +5-6
Defense Level: +2

Short Story: Leader has a friendship orb. Needs 2 friends in squad to help. Start at Elder, chat TWICE. Ends at Lady on Tower. (Up from Elder, Fly West past 2 statues, on the platform)

Easiest way to start: Just wait around West Archosour, someone will shout "Need 2 for FQ". Just join them and help them do theirs. When complete both helpers get an orb.

Chat Twice: Remember, after chatting to the Elder the first time. WAIT! You have to chat again before you fly off.

Quick 5k XP: Even if you don't want to beg for help, you can still quickly help someone do their FQ and SELL the orb to the Elder for 5000XP. 3 minutes work for free XP. :)