Right click with empty hand to mount. SPACE key goes UP. Letting off the SPACE key goes down. "W" key to go forward. "S" key to slow or stop. Left SHIFT to dismount.
Right-click with a random item to make him sit.
You can also shoot fireballs while riding your Dragon! The 'A' key shoots small fireballs and the 'D' key shoots big explosive fireballs.
Want to change the color of your dragon? You can feed your pet dragon a snowball to change him into a white dragon! Feed him a piece of coal to change him back to black!
Dragons and Baby Dragons can now act a little more civilized and not set everything on fire all the time. Right click with an Ice Block, and it's "flame off"! Right click with Flint and Steel to give them their mojo back (flame on)!
Dragons can be supercharged. Yeah. If you're feeling seriously destructive, right click your dragon with some Gunpowder! Explosive Fireballs! Wow! Click with Flint and Steel to switch back to regular Fireballs after you've thouroughly destroyed your surroundings...
If you really, really, really, miss your Baby Dragon, try right clicking your Dragon with a diamond. Poof. He will un-grow! And yes, a Baby Dragon that was un-grown can grow up again instantly if right-clicked with another diamond.
Where to find
Find them in the unstable ant dimension.