Veilfire runes are runes hidden away in dungeons and can only be found by shining veilfire on them (veilfire is a green, magic fire that wizards can use as torches).
I found my first in a dungeon near Master Dennets farm when you visit him to procure horses for the inquisition. The dungeon is
*** Spoiler - click to reveal ***in the mountains at the far end of the farm near the astrarium you can use to draw the constellations in the sky. Behind it is a river, follow it upstream and you will see two cave icons on your map. If you hover over them you will see that one of them is labeled dungeon. You will find it at the end of this dungeon (which is really short and simple).
At the moment I do not know how many veilfire runes are to be found in total, will update the solution when I find out. This game has an absurd amount of content so it takes a while to plow through it.