Typing the hats on a computer

Windows

Windows ships no Esperanto keyboard layout. You can add Esperanto as a language in Settings, but no layout comes with it, which is where many people stop and assume they are done.

And the US-International layout does not work. Its circumflex dead key composes with vowels only, and there is no breve key: ^ then c gives the caret and the c side by side. Zero of six. If you tried this and concluded you were doing it wrong, you were not.

What works: PowerToys Quick Accent. Microsoft's own free utility, with Esperanto as a built-in character set. Install PowerToys, open Quick Accent, enable it and tick Esperanto under Characters. Then hold a letter and tap Space (the default trigger; the Activation key setting also offers plain press-and-hold):

macOS

There is no Esperanto input source on a Mac, but there is something better: ABC Extended, which Apple already ships. Add it in System Settings, under Keyboard, then Input Sources. Two dead keys cover all six:

A dead key produces nothing on its own: press it, let go, then press the letter (shifted for a capital). Option+6 is easy to remember because ^ lives over the 6. Do not rely on press-and-hold: it offers no circumflex on c and no breve on u. For a custom layout, Ukelele is the free editor people use.

Linux

The only desktop that ships an Esperanto keyboard. The xkb layout epo (the command setxkbmap epo, or pick it in your desktop's keyboard settings) is the cleanest option on any system.

For everything else, set a Compose key (GNOME: Settings, Keyboard; KDE: Input Devices, Keyboard, Advanced), then:

The other circumflex letters work the same way, and capitals with the capital letter. As an escape hatch under IBus, Ctrl+Shift+U, then 109, then space gives ĉ.