Not only does your character have a friend at court played by another player, everyone has a certain amount of external influence they can bring to bear in negotiations. As we're unable to provide physreps for this cast of thousands, the system of influence is abstracted and represented by a personalised deck of twenty cards for your character.
If you are negotiating for a specific resource (or proof for a dirty secret), and you are unable to come to an agreement through other means, you can call upon your outside spheres of influence to put pressure on your opponent to hand it over. Your opponent then uses their own spheres of influence to defend themselves.
Charm (hearts) is your sway in fashionable circles, using your good looks, dress sense and social skills.
Capital (diamonds) is all about using your assets, cash or otherwise, to make an offer they can’t refuse.
Cunning (spades) might be using your influence by threats, extortion, thievery or deception.
Catholicism (clubs) uses your piety (or perceived piety) to bring the external influences to bear.
If you want to use your influence to insist that a resource is handed over:
These steps may be repeated as many times as the initiator has cards remaining. The defender may, for example, initiate a new negotiation for the resource they just had taken. They then become the initiator and repeat from step 1. The original initiator, if unsuccessful, may start a new negotiation immediately if they wish. It is down to you to decide how much influence you're willing to burn for one resource.
It is possible to regain influence that has been lost by roleplaying appropriately for at least 30 minutes then informing a referee so they can return your card to you. You may not gain more influence than you originally had (your influence score for that sphere).
To regain charm, do any of the following: Paint, embroider, play or listen to music, stroll in the gardens, read a book, etc.
To regain capital: Play vingt-et-un, place and win a wager, pose for a portrait, play croquet, play petanque, etc.
To regain cunning: Play chess, play backgammon, do a puzzle, study maps or charts, etc.
To regain catholicism: Read a bible, give or take confession, pray, sing hymns, etc.