Chivalry is most often encountered in the form of the Oath that Knights of the Four Orders swear on joining.
The core of it is the five knightly Virtues: Honour, Justice, Truth, Bravery, Devotion
They all blend in together a bit, so it’s hard to say exactly which virtue any particular bit of chivalry relates to. Most knights have different interpretations anyway, and different orders add extra bits in too.
Generally, though, a knight should always uphold his own personal honour, and that of his order. That usually means dressing smartly (except for Templars, who are happy being scruffy), being appropriately civil, keeping his word, and so on. He should be be just and fair at all times (though he will have his own ideas about what “just” and “fair” actually mean in practice), give respect where it is due (and perhaps not where it’s not) and should never lie. Some knights also look to avoid being misleading, or to actively spreading the truth around rather than just not concealing it.
A knight should always be fearless, and should always fight hand to hand, without using mage magic or missile weapons, and without any other unfair advantages like stabbing people in the back. Knights differ about how far this should stretch with things like attacking an enemy force in the flank, or fighting alongside archers.
Finally, a key thing about Knights is that they follow the will of the Gods, and Sidhe above all. Many knights will pay a lot more respect than you’d expect to Gods they don’t follow, though this is partly politeness.
Each Order has its own take on things, and The Grey Order in particular extends Chivalry quite a lot. It was after all they that codified it, and the others that adopted it from them (though it was built on generally accepted knightly behaviour). Following the basic rules of Chivalry doesn’t mean you have to be a pleasant person (see The Black Order), but to a Grey Chivalry includes things like protecting the helpless, giving aid when requested, giving fair hearing or judgement, not slaying a defeated foe, and being nice to ladies.
There is no set form for the Oath of Chivalry (it’s almost always sworn before a character starts adventuring), but the following has been suggested as a possible wording:
I, Insert Name, hereby swear fealty and do homage to the Crown of Ithron, to be a good knight and true; to be brave in battle and honourable in life; to strive for justice and uphold the truth; and to serve the Seven with devotion. May the seas rise up and drown me, may the skies fall and crush me, and may the earth open up and swallow me if I fail in this oath. This I swear in the name of Lord Sidhe the Allfather.