So, traits....
"Invoking" a trait means "narrate how your trait influenced the outcome of the test." Tell a story that includes your trait. Your LM may allow you to just say, "I invoke Anduin-lore" but you're missing an opportunity to make the game richer if you do that. Tell a story. Really.
Traits interact with AP in two ways:
BEFORE ROLLING: You can auto-succeed at the test/task if you narrate it using your trait, but you can't get any AP when you do this. Also note that LMs have the final say on whether auto-success is possible. E.g., somebody with Elusive might not be allowed to sneak up on a Nazgul, and somebody with Hardy can't simply skip every Fatigue check. Elusive doesn't mean invisible, and Hardy doesn't mean superhuman.
AFTER ROLLING: If you succeed with your roll, you can potentially invoke a trait to upgrade a success for a higher AP. That is, you can invoke a trait on a normal (no tengwars) success to describe how you succeeded in an "out of the ordinary way" to get a 2nd AP, or if you did get a great/extraordinary success you can narrate your "exceptional" success due to a trait in order to get a 3rd AP. (In other words, second AP is tengwar or trait, third AP is tengwar and trait.)
Finally, some of us houserule that the first AP can be earned for invoking a trait on a failure with an Eye. The rationale is that you learn from your mistakes, but it also helps new characters that might have low skills in some categories. And it's fun to narrate epic failure.
P.S. As Roc points out below:
I also completely agree with this, and although not perfectly RAW it is very much in the spirit of the prose. A normal success that saves the day against long odds should count as "exceptional".It's just my opinion but I think Loremasters should take the focus off of rolling Tengwars for AP generation and tie it more to narrative and trait usage. If a normal success greatly affects a scene and a player is able to tie it back to his character well, I see no harm in granting him a 3rd ap for it.