Sure! Let's say that your episode is a reinterpretation of a classic, and you decide that this is going to be "a modern retelling of A Werewolf In Paris". Your special guest is...a donkey.
The first Minor Arcana you draw is the five of swords; this card can represent conflicts, disagreements. In the context of our episode, you decide that what this means is that the donkey is being especially uncooperative in rehearsal, failing at hitting its marks despite being assured by the handler that it is a very well-behaved donkey. And you want it to be somebody else's problem, so you tell the Real Star; deal with it.
If the Real Star can suggest a solution to getting the donkey to act along (resolving the situation), they set aside a die. What size is the die? Entirely up to them. Could be a d4, d10, d100 even. This is the start of their individual dice pool. The solution a player suggests automatically works to resolve the solution, be it simple or complex. What we're interested in is having players contribute to the unfolding chaos by suggesting details.
Each player has an individual pool that is empty to begin with and is added to as you draw minor arcana; the rules on page 4 tell you that when the dice pools are rolled at the end of the episode (the six minor arcana you draw), you need to note the individual totals and then the overall total. So with three players you might each end with a pool of just two dice, or you might have been forced to resolve other situations and have additional dice, or have extra dice because a card relating to your Role was drawn.
And the reason the dice size is vague, why the result ranges are open to interpretation: you could play it safe and use a bunch of d6, or if you've only resolved a single situation you could gamble on getting a "high" result by choosing a d20. It's confusing by design, but there's nothing to stop the players from all agreeing to use a single dice size.
In the context of the show, you could work hard and do everything right but still fail to get your recognition because of a twist of luck.