In the third area "Molten Lands" in the "Steel Workshop" area (top right of map) you will encounter a dragon and a short cutscene (obviously) saying you should ride the dragon. Its a little wolf looking thing. Approaching it, you can hit "B" to ride it. I believe there is also a dragon on the way to Yarlanda's Mausoleum in Molten lands but I kinda killed that one. This one should be difficult to miss if you're fleshing out the whole map.
Pro Tip: If by this point you're playing with 100% accessibility and have also maxed out a weapon, the dragon is extremely weak. They do however drop gold when killed.
Happy Gunting!