There are two ways to bring your disadvantages into play.
1. Invoking a Disadvantage
This method is completely in yours, or the GM's hands. Anytime, before you make a test, you or the GM can suggest invoking one of your disadvantages. When this is done, you enter a Disadvantaged State, or add a Story Complication.
2. Critical Dice Failure "Snake Eyes"
Anytime you get a natural result of two on your dice roll, you and the GM must try to invoke one of your disadvantages, sending you into a Disadvantaged State, or adding a Story Complication.
If you can find no disadvantage that applies, you don't have to invoke a disadvantage, but you get no chance to earn a fate or survival point either.
If your snake eyes don’t already result in a failure, the GM can use the disadvantage modifier on the same test that caused the Disadvantaged State.
Whenever you enter this state, the GM gains a one-time ability to impose a -1d6 Disadvantage modifier to your current test, or a future test in the current scene. This choice can, and often should, be made by the GM after you roll, for maximum negative effect.
Disadvantage Modifier Rules
If you invoke a Fate point on a test, the GM can’t use the negative modifier for the same test.
The GM can’t use a Disadvantage modifier on a Defense test that has already failed.
The GM can’t use the modifier as a bonus to his own tests.
Once the scene ends, or the negative modifier has been applied, your Disadvantaged State ends as well. If the scene ends without the GM getting a chance to use the modifier, you don’t get a fate/survival point.
A Story Complication is more of a roleplaying disadvantage than a mechanical one. Your disadvantage leads to a twist, or an unfortunate turn of events that complicates your character’s life, and possibly everyone else’s. This might be your criminal past rearing it’s ugly head and spoiling your negotiations with the local law keepers, or a Dependant being among the hostages of an evil wizard you’re about to face. Story Complications should generally be agreed upon by both the GM and the players.
Refusing a Disadvantage
There may be times when you roll a snake eyes, or when the GM invokes, that you really don't want to be disadvantaged. You can choose to refuse the disadvantage for the scene without any penalty, beyond the missed opportunity to gain a fate or survival point.
There are three types of scene where disadvantages can be invoked. Many can be invoked in more than one.
Social disadvantages can be invoked when your character is in any kind of discussion or negotiation. Basically any time your character is interacting with NPCs. Most of the time, this is without weapons drawn and without attack and defense tests flying around. While this kind of disadvantage can lead to a Disadvantaged State, effecting social skill tests, it is more often associated with a Story Complication.
Combat disadvantages are the most cut and dry. They almost always take the form of a Disadvantaged State, and can be really annoying, but often just as entertaining and/or interesting. Certain combat disadvantages, like Crippled, should be invoked often by the GM and player, while others may only come up every once in a while.