The book gives details on how you loose Morality (Conflict)

But how do YOU determine how and what gains a character Morality?

The add-on adventure for the FaD Beginner Game has some tips, which basically sum up as "if a player does something in line with their Emotional Strength." Importantly, I don't think at any point does the game recommend granting more than +1 Morality, meaning its much harder to gain Morality than it is to avoid or gain Conflict, which fits with the way FFG presents their Morality system

A die roll determines Morality. I wasn't aware of any other ways to gain or lose it. Anything done in the Beginner Game adventures is typically unique to those games and are not a representation of the "real" rules.

I hand out Conflict, or perhaps I should say opportunities for Conflict, with a generous hand. Then it's up to my players how much Conflict they want to take and what sort of modifiers they'll get on that end-of-session D10 roll. Their Morality goes up or down depending on that roll. I never give (or take) Morality straight up; it's all determined by the Conflict roll.

You are supposed to give conflict for specific actions, then if the character engaged their strength/weakness, they roll 1D10 and modify it by the conflict. That is how much their morality goes up or down.

The book recommends not rolling if they are not gaining conflict or engaging their strength/weakness as that can quickly get them to 80+.

Funny side note, in a game I played some years ago one of the other players had his son playing with us. In one mission we were told to take an assassins ring, filled with poison, and kill a person in cold blood. While most of us wrestled with the moral conflicts of killing a person in cold blood even though we had all manner of files showing him to be a monster the boy said "What moral conflict? Give me the ring." That became our battle cry after that...

Essentially, if your campaign uses Morality then it means that you are making the PCs' actions and the personal CONFLICT (heehee) of such actions a central part of the story. As a result, the GM should always make sessions full of opportunities to gain conflict. This can be anything from tangible temptations such as credits, equipment, ships, clothing, or what have you that comes at another's expense to killing, fighting, hurting others when there are other ways to solve the situation all the way to the more personal temptations that play with the weaknesses or test the strengths that the characters have. At the end of session you then have each player roll a d10 against the conflict they accrued during play and that determines how much they lose or gain. It is in fact much easier to lose a lot of morality than it is to gain a lot since there is a cap of gaining at 10 points (if 0 conflict) but there is no cap on losing (conflict can go above 10).

Also, Rowdyoctopus is partially mistaken, on rolling at end of session. You do roll 1d10 (as above) but you roll no matter what (unless your character literally had no chance to gain conflict, which happens sometimes). As far as engaging goes, it's a completely optional rule which if used allows for double the loss/gain of morality at end of session if the PC engaged their strength or weakness and only if their morality triggered at the session start. That is, rolling their exact morality rating. If rolled, then it's up to the GM to give them a chance to engage their strength/weakness and then if the player takes the chance to make a significant choice either way they then double the gain/loss that results at the end of session.

Say the beacon of light of the party had his morality triggered at the start of a session during which he accrued 2 conflict. The GM made sure that during play he was given the opportunity to murder the BBEG who had surrendered and was helpless (Anakin to Dooku in Episode III), but instead the player took the oppertunity to play to his strength of Compassion and let him live because he believed that the BBEG could still be saved and turned back to light. Now he rolls a 6 on his Morality check and as a result gains 8 Morality instead of the normal 4 because he successfully engaged his strength that session.

Side Note:

Kinda unrelated but I just wanted to bring up that I've noticed that it is strangely common, especially on the F&D forums, that Morality is a strictly force driven mechanic and as such shouldn't affect those not force-sensitive or affect those who are droids as much as it affects force-sensitives if it affects them at all. It's true that those who use the force have an easier time accruing conflict as they have the oppertunity to use Dark Side pips, usually find artifacts and/or holocrons that could be tainted as major personal development arcs, etc, but otherwise PCs are all treated the same. No one should be made to have a mechanical advantage or disadvantage based on their type of character as morality has benefits and penalities not only for the individual character but for the party as a whole as well. No matter what central mechanic you run, whether it be Obligation, Duty, Morality, or some future mechanic, all PCs should be equally affected.

It's worth noting (although a borderline falacy) that FFG's Morality system is almost an exact carbon copy of KoTOR's (moreso KoTOR 2 or SWToR's) Alignment system. All characters, including droids, have scores and can gain or lose based on their actions. It's much more about how the characters affect themselves and those around them and less how the characters are affected by some supernatural force. All in all It's your campaign, so run it as you see fit.