Packages to enable Estonian ID-card support are available from AUR (Arch User Repository) and can be installed via yaourt. This article explains how to install the official software versions by AS Sertifitseerimiskeskus.
Long story short: install yaourt, then run as root:
yaourt -S esteidfirefoxplugin qdigidoc qesteidutil pcsclite systemctl enable pcscd.socket
Browser plugin (web authentication & digital signatures)
It also requires you to run the PCSC daemon, which is included in official repositories.
pacman -S pcsclite
If you're running systemd, you can make it auto-start on demand with the following command:
systemctl enable pcscd.socket
If you are still using old SysV init, you have to add pcscd to the DAEMONS array in /etc/rc.conf:
Don't forget to restart Firefox after finishing.