I have yet to run FATE myself, but I have also purchased the Core book. One of the hardest obstacles you're going to encounter is this:
It's not D&D.
I mean, yes, you COULD run a dungeon crawler and build in all sorts of monsters to hack and slash and blow up with arcane and divine powers...
But that's not what it's for.
FATE is a role-playing system that I would almost call the 'opposite' of D&D. Where D&D focuses on numbers and stats and gradual improvement and looting, FATE focuses on scenes and 'tags' and really getting into what makes a character, nay, a persona do and act the way it does.
I'm betting the 'tags' are going to be the hardest part for most people to grasp. My suggestion is to explain to your players that tags are like meta-objects that are interactable and mutable, depending on what players do or don't do with them.
Also, be generous with FATE points and encourage your players to use them. FATE points are the player's way of building the story the way THEY want. As the GM, you're not running a story 'against' them so much as building a story WITH them. They should be allowed input into each scene, and FATE points are a way of guaranteeing that.
Other than that, GLHF (Good Luck, Have Fun!) and let us know how it goes. I always look forward to hearing examples of FATE in play.