Q:

How do I know which key combination does what for the Dvorak international alternative layout?

So far, I can only figure it out by trial and error.
Right Alt + a = à
Right Alt + o = ô
Right Alt + e = é
Right Alt + u = û
Right Alt + i = î
Right Alt + 4 = €
Right Alt + , = ä
Right Alt + . = ê
Right Alt + p = ë
Right Alt + y = ü
Right Alt + ; = â
Right Alt + q = ö
Right Alt + j = è
Right Alt + k = ù
Right Alt + x = ï
Right Alt + c = ç
Right Alt + ` = dead `
Right Alt + 9 = dead `
Right Alt + ' = dead ´
Right Alt + " = dead ¨
Right Alt + < = dead ˇ
Right Alt + > = ·
Right Alt + p = dead ¸
Right Alt + 6 = dead ^
Right Alt + ^ = dead ^
Right Alt + s = ß
Right Alt + ] = dead ~
Right Alt + ~ = dead ~
Right Alt + Q = dead ˛
Right Alt + : = dead ˝
Right Alt + J = dead ˝
Right Alt + C = dead ˙

Right Alt + Q - Right Alt + X = Ǭ

There's more, but I haven't figured it out.
[update]
Thanks to Stephen Kitt, I solved it:
[me@MyComputer ~]$ sudo pacman -S libgnomekdb
...
[me@MyComputer ~]$ gkbd-keyboard-display -g 1

A:

You can see the full layout definition in /usr/share/X11/xkb/symbols/us on your system. Looking at the current upstream version shows that, e.g.

the top-left key produces ` (dead), ~ with Shift (dead), ` with Alt (not dead), and ~ with Alt Gr or ShiftAlt (not dead)
the next key produces 1, !, ¡, ¹ respectively

and so it goes.
If you’re running GNOME, you can use the key map applet to view the full keymap:

