Page 87 contains pretty much all you’ll need. I’ll clarify further in response to your questions.
- As I understand, if you spend Determination point on one session, it will be replenished at start of another session.
- You get one point of Determination at the beginning of each session. If you spend all your Determination in a session, you’re still getting one point to start the next session with. If you spend more than one Determination in one session, you’re still starting the next session with one point. Spend 'em or lose 'em. It probably would have helped if there was a statement along the lines of “Determination points do not carry over from session to session” somewhere in the book. I’ll note that for future reference if we decide to make a second edition someday.
- What about extra Determination points, received by challenging the Values? Are they lost if not spent until session ends?
- The intent of the rules is that if you’re challenging a Value, you’re receiving a point of Determination to spend immediately (p. 87-88). Challenging a Value is tied to some task ( Once during a mission, if a character has a Value which could affect a Task or situation negatively, they may challenge that Value.) so it’s not saved for later–it’s spent immediately upon challenging the Value.
- Is there a way to cumulate more than 1 Determination point, other than using Values?
- Sort of. See page 87, right column:
" If the character is in a situation where one of their Values would make the situation more complicated or more difficult, the Gamemaster may offer the Player one Determination in exchange for suffering a Complication"
In this case, there may not be a Task associated with this; it might be a roleplaying scene where a Value might come into play, but not be tied to a die roll as such. The example text in the core is a good one. Worf makes a choice that has nothing to do with a die roll, and the Romulan dies because of that choice. Worf’s Player now has an additional Determination point to spend during the session.
One possible other way to gain back a point of Determination is to be a Veteran officer (p. 118):
Whenever the character spends a point of Determination, roll 1 . If an Effect is rolled, immediately regain that spent point of Determination. The character has a rank of at least Lieutenant Commander.
The only other way to gain a Determination point, or more specifically the effects of spending one, is to save a Milestone and then spend it in a subsequent adventure (p. 139).
At any point during any subsequent adventure, the Player may call back to that saved Milestone and the adventure it came from. The Player describes how a memory of, or lesson from, that adventure relates to the current situation. If the Gamemaster approves, then the Player gains the effects of a point of Determination, as if they had used a Value or Directive in a positive fashion. After this has been resolved, cross out the saved Milestone — each saved Milestone may only be used once.
Hope this helps!