Enable it
GNOME: Settings → Keyboard → Special Character Entry → Compose Key → pick Caps Lock or Right Alt. KDE: System Settings → Keyboard → Advanced → Position of Compose key. Others: setxkbmap -option compose:caps (Caps Lock becomes Compose; Esc still works via tap in Vim-style setups).
The 10 sequences that cover 90%
Press Compose, release, then type two keys. e ' → , e ` → è, u " → ü, n ~ → ñ, c , → ç, o c → ©, o o → °, << → «, >> → »; s s → ß. Order rarely matters (both 'e and e' work).
Ctrl+Shift+U: hex for everything
Press Ctrl + Shift + U, an underlined “u” appears, type the hex (20AC), Enter → €. Works in GTK apps (GNOME Terminal, Firefox, gedit); Qt/KDE apps vary — Konsole historically ignores it, Kate obeys. Every character page lists the hex in its Linux row.
Custom sequences
Add your own in ~/.XCompose: <Multi_key> <e> <u> : "€" then reload. Compose files are plain text, version-controllable dotfiles — the Compose key is infrastructure, not a trick.