Repairing equipment

There are 2 ways of repairing:
Standard repairing in the repairshops
Using a Mysterious repair ticket

Standard repairing
The standard way of repairing equipment can be done in the Repair shops of the cities Bluebird, Rainbow City, Goldburg, Baghdadand Emerald City. Just talk to the right NPC to repair your equipment. NOTE: Books can only repaired in Bluebird.

Repairing an item lowers the maximum durability. It takes the mean or average of max durability and current durability available and gives you the middle number. Example: Max dura 1000, current dura 500. The mean is 750, this will then be the new Max durability. Actual values can differ slighty from this example.

The costs of repairing an item are (or close to): (Item Value in store*4)*% of Durability Difference.
So lets say you are repairing a generic Level 20 equipment (2000 value) that has 1/200 durability remaining.
That means it takes (2000*4)*99.5%=7960 coins to repair. (199/200=99.5%)

What should i repair?
Obviously it is a lot more expensive to repair your level 20 standard boots from the store than to just buy new ones.
For handmade gear it depends on your own judgement. You have to way the costs of repairing against the costs and time to make a new piece.
Special gear (fantastic, Dreamy, Dreamlike, Legendary, Sin and Lost Sin) are the obvious items you want to keep. These are for most people hard to replace and so you will repair these items quite often in your Fairyland career. :-)

Repairing workdolls
Note that it is also possible to repair workdolls this way!
Mysterious Repair Ticket
There is not set location to use a Mysterious Repair Ticket. You can use it anywhere, but not anytime.
You have to repair the item at least once the standard way, to be able to use the Mysterious Repair Ticket. Some people have experiences that involve repairing the equipment multiple times the standard way before they can use the Mysterious Repair Ticket. So don't be alarmed if it won't work right away for you.

Using the Mysterious Repair Ticket will restore the durability of the item to it's original maximum. So if after a few times repairing it the normal way the new max durability is 200 in stead of 2000, using the ticket will restore it to 2000/2000.

Using the ticket involves no costs. Of course getting it will. You can buy it from Lager's Item Mall, or try your luck at the market.
Thanks to Helreginn, GeminiRage, Nishihara, Seraphim, belzeneef, Moiraine