Welcome. I'm running PotA right now. Here's what I think will help in addition to all of what others have said.
1) Understand that the adventure is sprawling and there are many, many possibilities...but don't let it overwhelm you. To that end, before each session make a tiny flow map of possibilities or events/encounters that you can run to help the players make decisions. I'm finding that because the threat from the cults takes time to develop, the players have a hard time remembering clues and deciding which direction to go. Although I don't condone railroading (making players make specific choices to follow the story), I do add in and run certain events/encounters at times when I feel as if the party has come to a dead end...so be prepared for this.
2) Also, before each session, when I make my outline, I also pre-think how NPCs/Monsters will interact with the group. By and large, there is some guidance in the adventure, but never truly enough so don't be afraid to make each interaction and encounter your own. Specifically plan how the prophets will act when they encounter the PCs. Pay attention to personality descriptions. For example, Aerisi is overconfident. Use the small guidelines in the book to build upon.
3) Realize that the first level or so the PCs are really fragile so you may have to have contingencies for when players go down or die. Also, realize that the cult strongholds are not equally challenging. Here's the order of challenge level: Feathergale Spire (air), Riverguard Keep (water), Sacred Stone Monastery (earth), Scarlet Moon Hall (fire) - and the temples are also ordered that way in terms of difficulty too. If you run the Moving Stone Temple part of the adventure in Red Larch, the PCs will encounter a priest of The Black Earth (earth cult) so it is quite likely that the players will want to investigate the earth cult first. This could be tough. In my games, I had them encounter the Feathergale Knights fighting with a group of Black Earth cultists so that the party could decide to join the fight to help the Knights. After this, it was natural that they would interact with the Knights and then go to Feathergale Spire. It made the transition smooth and kept them in a more comfortable challenge potential. That said, the adventure is a sandbox, so it is perfectly ok for the party to encounter challenges above their level. Just make sure the players know that this can happen so that they know when to run or avoid combat. Telegraph through description so that they have more clues about the difficulty of any given encounter.
Overall, I like using the adventure as a backdrop for my campaign and I like to add my own touches as PCs and the story develops. Don't be afraid to make it your own.
Good luck.
Cheers.