For the sake of ease of writing this i'm going to assume that you a) play WoW and b) know how to play your character and c) know what an elite is. Please donÔÇÖt try to attack this mob until you are 80 or have a friendly 80 player who will sit patiently for the hours that this will take, kill the mob with you, and then not want the reins. Good luck finding one of those!
The reins are dropped by, not surprisingly, the Time-Lost Proto Drake which is a very rare spawning elite dragon, a Blue Drake. There is a less rare (but still elite and rare) dragon called Vyragosa, that seems to share the same wandering patrol paths in Storm Peaks. Vyragosa hasnÔÇÖt been seen at the same time as the Time-Lost Proto Drake and appears to share the same multiple or random spawn points, so it has been assumed that the Time-Lost Proto Drake is effectively a spawn of Vyragosa, however this has not been verified by Blizzard (WoWÔÇÖs creators) who state that the spawning time and place of Time-Lost Proto Drake are random.
Time-Lost Proto Drake spawn sites and patrol
Because of the many recorded spawning spots for both the Time-Lost Proto Drake and Vyrgosa there isnÔÇÖt truly a site to sit and wait for a spawn as there are with so many other WoW mobs. But the areas that this mob moves in are known, and it travels around the Frosthold and Brunhildar Village in the south west of Stormpeaks, Terrace of the Makers, Ulduar, The Snowdrift Plains and The Temple of Storms, just about the entire west side of Stormpeaks. There is no official route for this mob either, becuase it is so rare it's been very hard to ascertain what directions and routes are being taken, the few comments and experiances that have been shared seem contraditory, and so suggest that the directions and routes taken are also radomized.
Addons for rare mobs
As it is so rare you will probably have to spend a lot of hours waiting, so clear your diary, put on some good films or music, get healthy snacks at your PC to see you through, chose your spot and sit and wait it out. The frozen lake at Bor's Breath, and Engine of the Makers are good places to try but if you see anyone else hovering around you then either move to a different spot or be very diligent. You are not the only person hunting this mob, and while much WoW drama can be caused by "stealing mobs" you want to be the cause here, not the drama queen. The drake will be flying, at anywhere between 20 and 70 yards so sit flying on your mount for the best chance of seeing her.
There are addons that can help you spot the dragon more quickly. Silver Dragon is a great addon that can be downloaded from Curse.com, which spots and notifies you of any rare mobs in your area. Or a macro (/tar Time-Lost would do it) that you could spam click or button mash (depending on play-style), which would at least give you something to do while you wait.
When you actually get to meet her....
Should you be lucky enough to catch this beastie she casts 2 different spells, Time Lapse, that stuns and does nature damage (369-731 damage per hit) and Time Shift which teleports the dragon away from you and cleans all your debuffs off her. SheÔÇÖs only got 18,900 health so is easily solo-able by an OK geared level 80.
Happy dragon hunting, and try not to be mean to anyone feeling robbed of their mob if you do get her... remember they could have been waiting for days.
I am using this macro, because I find it useful:
/target Time-Lost Proto Drake
/target Vyragosa
/stopmacro [noexists]
/tell YourNameHere >%t<
If you find the Time-Lost Proto Drake or Vyragosa, you'll get message from you. Pick up your weapon and kill it!