Epic Fantasy is a big part of role playing games, and of the Science Fiction and Fantasy works that inspire them. It doesn't matter if you're talking about the grim-dark far future of Warhammer 40k, the classic high fantasy of Tolkien and Middle Earth, or a fusion of both dark and the fantastical like we see in George R.R. Martin's Song of Fire and Ice. Worlds and stories that fit the Epic Fantasy title are all around us. So how do you bring that feeling to the table?
It Is All About Scale
The trick, the only real trick, to making something go from "Fantasy" to "Epic Fantasy" is the scale of what is going on. Epic fantasy is, by definition epic. It is huge, and everything in it is huge. The stakes start at the fate of the world and go up from there. The tiniest of set pieces begins at grandiose and scales all the way until we don't even have words for what we're looking at anymore.
This scale is the thing you need to remember whenever you are handling something you want to be Epic. But especially in these three points: stakes, landscapes, combats.
Like I said, in Epic Fantasy the stakes are always at the very least the fate of the world. Sometimes it is much more than this. If your story doesn't involve some threat that will wipe out all life/culture as we know it and begin an era of darkness that will last for centuries than you probably aren't quite in the Epic market yet.
Fortunately, this is actually the easiest of the three things to skip and have no dire consequences to the feel. The stakes need to be epic for an epic story, but it is perfectly possible to have a non-epic story set in an epic world. In fact, the stories I referenced above are full of non-epic stories.
Even then though, you want the epic stakes to be in the background. It's one thing for the dwarf and elf to make friends and become the firmest of companions. It is an entirely different thing for that to happen as they struggle to do what they can to save the world, testing and proving that bond time and again through out.
Fights in Epic worlds are just bigger. You seldom get a one on one fight, unless the two people in the fight are both masters of their work. The kind of masters where the only one who could hope to stand against that person is the one in the ring with them. Beyond that, you have swarms of enemies, armies of good guys, and action scenes that would make Michael Bay blush to fill the gap.
This one is all on you as the GM. To pull this off you need to manage the challenge of your combats with the precision of a neuro-surgeon. A degree off to one side and you will wipe the party. To the other side and you risk turning epic into absurd and farcical.
To pull this off I'd recommend watching movies more than reading books. Both are great, but movies will give you a better idea of the eye-candy you want to invoke with your words. The Lord of the Rings movies are great for this - even the Hobbit movies can be useful - and they'll give you an idea of the kind of visuals you want.
Epic Construction and Landscapes
This is perhaps the most important thing for an Epic world. Human history is full of forts with impressive 20' high walls, seven story castles, and armies that numbered in the thousands. It wasn't until King Louis XIII of France that humanity saw armies hit the 100,000 mark.
Epic Fantasy on the other hand has castles with walls that are 200 feet high or more, castles that pierce the very heavens with their height, and armies that number in the millions, before we get to camp followers and supply trains.
Beyond this, Epic Fantasy has giant statues, monuments to ages gone by, and landscapes that could only come from the wildest imaginings of a painter. Why? Because it is epic.
This is what you need most for your world. If your players don't believe that the scale of everything around them is to this degree they can lose the feeling of being in an epic world. So make sure to capitalize on it.
In short, the scale of an Epic world should, objectively, make people feel very small. The numbers arrayed against them seem hopeless, the size of everything is bigger than them, and the power of magic is insurmountable. And yet, they are able to rise to the occasion. Those giant buildings and constructions are a testament to the ability of heroes and the good people of the world. Those numbers can be driven back into the darkness by a hero who is brave and bold enough. That power that seems so insurmountable is nothing compared to the love and friendship that is shared between those arrayed against it.
It's all a mater of scale, and while the numbers are huge, managing the balance of the scale is how you control the kind of fantasy beyond epic you have.