There are those who make money by taking advantage of the gullibility of others. These people range from teenagers who ask for change on street corners so that they can afford a new pair of designer jeans to people who spend weeks working a "mark" in order to deceive them into giving away huge sums of money (the excellent movie Dirty Rotten Scoundrels is about the latter type). Bums, hobos, tramps, and others who beg for their living do not generally fall into this category, as they are not trying to con anyone (they really do need the money).
When a character makes a con attempt, the GM will assign a difficulty rating depending on what the character is attempting to get. Players who give a dramatic presentation of the con attempt (some GMs may require this) may earn a bonus, depending on how convincing their approach is; however, characters should not be penalized because their players can't act.
If the skill check is successful, the mark is usually allowed an INT check, with a negative modifier of however much the Con Artist skill check succeeded by.
Dirk is caught stealing (see Pickpocket skill example). Being manhandled by his captor, Dirk cannot concoct a good cover story, so the GM gives him no bonus to his Con Artist skill level of 64. He rolls a 42, succeeding by 22(=64-42). The guard has an INT of 48, so makes a check against 26(=48-22). He rolls a 57, and falls for Dirk's lame excuse. Dirk spends his earnings discreetly.
Other skills may modify a character's chance of success. See the example in the Disguise skill description for an example of this. The GM is the final authority on whether two skills complement each other, and what effects this may have.