I purchased the AotR core rulebook yesterday. I've been trying to understand duty. It says that when a groups combined duty reaches 100 they get a reward, yet I have not been able to figure out how they gain Duty. Could someone direct me to where I can find this information?

Unfortunately, there's nothing in the core book to suggest how much Duty the PCs should earn, either for fulfilling their Duty or just in terms of general Duty awards.

Back when AoR got released, the designer in charge (Andy Fischer) made a suggestion on the Order 66 podcast that the PCs should generally earn about 5 Duty each per successfully completed mission/adventure, with a few extra points earned if they accomplish something that falls in line with their Duty.

Depending on the size of your group, this means that the PCs will get a Contribution Rank increase about every 4 or 5 adventures, possibly sooner if they have chances to fulfill their respective Duty.

Thank you very much.

It really depends on how fast you want the PCs to advance in rank.

I'd recommend working backwards from 100: figure out how many sessions you want to pass before your heroes' Contribution Rank increases, and then award Duty as appropriate to that calculation.