How do I change between orders? (Durmand, Whispers, Vigil)

TL;DR - You can't change order.

Before and shortly after game release there was rumors that you can change your order becouse of old Wiki page about Order that sayed that player "would be able to change Order with a little bit of effort".

It was written in disscusion on this page this information was mistake and "choice seems to be tied into game mechanics".

Source of this missunterstanding is quotation from Ree Soesbee, GW2 Game Designer who was missunderstanded as she said;

The choice of an order is not compulsory, however, you can’t progress through the full extent of the storyline unless you do so. You can change orders once you’ve chosen one – with a little effort – but parts of the storyline are linked to the orders, so in order to see certain facets of the personal story, you will need to join one. That said, you can play the game without joining one if you truly choose to do so.

But true undesrtanding of this statement was explained few posts later;

You can get through the all major areas in game, but not through the whole story. You can do dungeons/events level up and visit every part of the world - except your personal story will stop progressing.

And;

So I could play 99% through the story (but not finish it) with order A, then switch to order B, and do 99% of its story, and then order C?

You won't be able to do that.

Once you choose an order, YOU CANNOT change to any other. That order is what your character's storyline will follow.

You can create a new character, and in that story choose a different order, but it will not change what the previous character's choice was.

Quoted directly from the Guild Wars 2 Wikia:

Other players can help with another player's story but are not able to make choices which affect the outcome, though they can choose to accept the outcome as their own.

I suppose that by choosing another storyline, you can change your order, if your comrade chooses one that is different from your own. Unfortunately, I have not yet discover how to do that.