There are 2 ways to ride the ender dragon first is a summon.

How?:Do the command
/summon MinecartRideable ~ ~1 ~ {Riding:{id:EnderDragon},Invulnerable:1}
This will summon a minecart that is invincible riding the enderdragon!
Then you can chase it down then ride on it!

Next way is to use a third party program called NBTExplorer.

How?:First open up minecraft and put a boat in water, ride it.
Exit then Open NBTExplorer, open player.dat and find the string Riding.
Edit the value to EnderDragon.
and viola! you are now riding it with full control!(Just the 2nd step, not the 1st...)

Leave a diamond, sub or at least a fav if this helped.