I remember something about people gaining powers from areas that were once inhabited by dragons. The main character can talk to animals and is followed around by a wolf; her brother can influence others. They meet a noble later on who can see into the future through skin contact. There was also something about a draft for the "Talents" to send them off to war.
I was just looking for a book that meets this description too. I think it's The Secret of Dragonhome by John Peel. I also just discovered that he wrote a sequel (The Slayers of Dragonhome) to this book in 2011. Hope this is what you're looking for!
Melayne and her young brother Sarrow are Talents, hunted by the King's relentless Seekers. If their Talent is discovered, they will be sent to their death. So they must hide...or die.
Melayne and Sarrow find refuge at Dragonhome, the mysterious estate of the shadowy Lord Sander. Lord Sander also has something to hide--a dark and fantastical secret that haunts his every move. In order to save herself and her brother, Melayne must confront forces much stronger than her talent--tempests of magic, desire, and betrayal. If Melayne is not careful, her truth will be revealed.
Melayne must unlock the secrets of Dragonhome. As danger approaches, it will be her only hope
From one of the reviews:
The protagonist, a girl named Melayne, has a magical ability called a Talent that allows her to communicate with animals.
Perhaps you are thinking of the Xanth series by Piers Anthony? The magic system is based around "talents" that many people have, that allow them to do things such as seeing into the future, and a plethora of other things. In the over 30 books in that series, it is possible a main character is followed around by a wolf, but I can't remember.
As for dragons being the source of their magic, in the Xanth series the source of magic is a demon. However, he occasionally appears in the form of a dragon, perhaps that is what you thought of?
Might be way late, but I'm pretty sure you're talking about Assassin's Apprentice by Robin Hobb
The magic is passed down by bloodlines, it's called The Talent. And the protagonist has a rare combination of The Talent and an ability to connect with animals. The rest of the trilogy goes well into the dragon lore.