When an ability or effect grants your Favored or an enemy imposes Hindered, you add or subtract 1d6 from your d20 roll. The ability or effect would mention to what extent the Favored or Hindered applies.
If you had Favored on the roll and rolled a 6, that increases your degree of success by 1 step. So if you rolled a success and got a 6 on your Favored die, you gain a crit instead. Conversely, rolling a 6 on a Hindered die will reduce the degree of success of the roll by 1, turning that success into a failure.
You can only have a maximum of two Favored or Hindered on your character at one time, even if they are on different types of d20 roll (i.e. attack rolls and ability checks).
Stacks of Hindered cancel out stacks of Favored but only on the same d20 roll. So if you are Favored on your attack rolls and an enemy causes you to be Hindered on attack rolls, the effects cancel out and you gain no bonus to the roll.