How do you get a dragon head in Minecraft?

You can find Dragon Heads on End Ships.

How to locate an End Ship

After you kill the ender dragon, you might spot two clusters of bedrock with a portal in the center off the edge of the island- these lead to the outer islands of the End. The portals look like this:

It's extremely hard to get in them, as you can see the gap for the portal is only one block tall (use of an ender pearl is recommended!). If you can't, the outer islands are ~1000 meters away from the central island, so lots of stacks of some easy-to-obtain block like dirt or cobblestone could get you there too. Also, you can make a flying machine., make it go outwards from the islands, and AFK for a few minutes. The outer islands look like this:

As you can see, there are many dips in between the islands, you'll need a lot of blocks. Eventually, you'll come across this:

which is an End City. Up in the air, you might see an end ship:

On the very front, you'll see a Dragon Head...Feather Falling is extremely recommended!

Thank you for the suggestions, commenters!

According to the wiki, dragon heads will generate on End Ships. To quote:

A dragon head can also be seen at the bow of the ship, making this currently the only natural way to obtain the beast's head.

End Ships can be found in an End City, which randomly generate on outer Islands in the End. To quote:

End cities naturally and randomly generate in the outer islands of the End, which are accessible via the end gateway portal that generates after killing the ender dragon. They are fairly rare; one can travel for thousands of blocks without encountering a city.