Disposition is the rating of how much a character likes the player, ranging from a character not liking the player (at 0) to a character being the player's best friend (at 100) (in Skyrim, the system works differently). Disposition is based on a number of factors, including race, personality, reputation, faction affiliations, and past encounters with that character, their friends, and their enemies. Disposition can also be affected by the speechcraft skill or through the use of charm spells.
Speaking with a character causes the camera to zoom on their face. Once this occurs, several options can be taken. Disposition can be seen by clicking the icon with the face. From this menu, disposition can be altered by selecting Boasting, joking, admiring, coercing, or bribe from the colored wheel. The number in the center of the wheel marks the character's current disposition.
1 coin raises disposition by approximately 10 points, depending on the speechcraft skill; higher levels grant higher bonuses. The amount of disposition granted by each bribe lowers every time it is performed, until the maximum amount of disposition is reached.
An important factor in persuading is their facial expression and the amount of orange filled in the options triangle. For example, when speaking to a Khajiit, if they do not like the option that the player is about to select, they lower their ears and hiss. Hovering the cursor over the "Joke" option causes this response in Khajiit, as many of them do not appreciate humor. Pursuing a persuasion option that the character does not find appealing lowers disposition.
For maximum effect, try and choose the option most filled in by orange. Pick only the options that make characters appear most pleased. If that option is filled in with the most orange, then more disposition is awarded. After choosing an option, it cannot be selected again until the others are exhausted. The orange triangles transfer clockwise through options.
Charm spells, governed by the Illusion school of Magicka, influences disposition, albeit temporarily. The magnitude of the spell increases disposition by that much for the duration of the spell. It is possible to purchase or create charm spells potent enough to raise anyone to maximum disposition long enough to sway their buying power, complete a quest, or extract secrets from them.