These rules were originally created for the character Katie when she gained Dissociation after getting back from the Rat House. They're general enough to work for any character who gains the derangement, and are pretty straightforward.
The Dissociation derangement is based on Situation-Specific Dissociative Amnesia and is in the same family as DID. Where a person with DID creates multiple personas to deal with trauma, a person with Dissociation simply forgets those events. Under stress, they cut off that part of their memory and make up some fiction to fill its place. This fiction is always believable and entirely plausible, as long as you don't look too closely. Dissociative amnesia is rather common in cases of severe or repeated trauma and is one of the oldest recognized disorders, dating back to Pliny the Elder.
That said, we aren't technically using dissociative amnesia. Dissociation as written here is a creative interpretation of that disorder's hallmark symptoms. It is a Mild Derangement for the purposes of game mechanics.
Every sufferer of Dissociation has experienced severe or repeated trauma at some point in their lives, and simply cannot accept it as part of their being. So, the first step for fleshing out a character's Dissociation is to figure out what sort of trauma they're coping with. Some examples are: witnessing the murder or suicide of a loved one; sexual abuse as a child; or military combat, typically when things go wrong. One rule of thumb is that this trauma is something your character desperately wanted to forget, so he did.
Once you have a good grasp of what your character is repressing, you need to find out how deep that repression goes. A good question to ask is, "Does it cover nothing but the actual traumatic event, or does it kick in for other similar events?"
If it fits for your character, you can pick more than one trauma which triggers this derangement. Just make sure you have a good reason for all of them.
For a quick example, take a 14 year old daughter to a relatively happy couple. One morning, she comes downstairs and watches her mother tip off a chair, snapping her neck in a homemade noose. To no one's surprise, the daughter develops Dissociation. In her case, it's important for the player to ask, does she dissociate only about her past and her mother? Does she have an episode whenever someone's standing on a chair? What does she do if she sees a noose?
Whenever your character is faced with something which might trigger his dissociation, he must attempt a Resolve + Composure test to avoid a dissociative episode. If he gets any successes, he is able to avoid dissociating and can handle the trigger without too much trouble, though he may be flustered. If he fails the roll, his dissociation kicks in. This means that he immediately and unconsciously concocts a plausible set of lies about the world which, were they true, would make the offending situation, event, or memory impossible.
Ex: Someone whose dissociation was triggered by "not knowing where a loved one is" might immediately believe, "Dad's back at home, probably watching football again", when her father is two hours late to meet her somewhere.
Your character believes this fake version of the world with absolute conviction, as though it were the real thing. Any new information that doesn't fit prompts him to add lies until it does fit. If at any time that becomes impossible, or his world becomes self-contradictory (or he has a sudden insight into what's going on), his symptoms might worsen. Unless the thought of past occurrences is a trigger, your character comes back to himself entirely once the dissociative episode is resolved. In an odd twist, he now cannot remember any of his delusions. Instead, he'll recall the situation with normal accuracy, though he may not be able to explain his actions.
If a dissociating character's fake world is challenged enough, the character must make another Resolve + Composure test. If he gets even one success, he breaks out of his dissociative episode and can deal with the situation/event/memory rationally. If he gets no successes, however, he still technically ends his dissociation, but it is replaced with something worse. This can be an OCD-like routine associated with the trauma he was repressing: checking all known residences of someone, making sure every door is closed and locked, etc. It can also trigger a different derangement that your character has, as long as it makes sense. If he doesn't have any other derangements which work, assume he slips into an OCD routine. You should figure out what happens in this phase beforehand.
Dissociation is one of the few derangements that can adapt and change over time. As your character goes through life, they can apply Dissociation to new traumas that scar them and overcome older ones. This is not a whimsical process, however, and you should think carefully before deciding that a traumatic event gets added to your character's dissociative zoo. If you decide to go for it, back up your decision with good reasons and good role play.
In a more typical game play sense, Dissociation can be upgraded to a couple of different severe derangements, depending on what fits both the character and the circumstances. Most commonly, it can turn into full-blown DID, OCD, or Dissociative Fugue. As written above, Dissociation already has some elements of OCD built in, so that might be a natural progression when old traumas are reinforced. DID is a more likely path if things get so bad that the character's psyche fractures under the stress, which probably requires new, extreme traumas. Dissociative Fugue is only on the table for NPCs, since it involves a complete loss of personal identity and can last from a few hours to a few days, or up to a few years at the extreme end.