Additionally to the standard packages which you would install like so from the standard repository of Fedora:

sudo yum install qesteidutil qdigidoc mozilla-esteid

you should also install the pcscd package:

sudo yum install pcsc-lite

Finally, some useful tool here:

sudo yum install pcsc-tools

Source: http://symbolik.wordpress.com/2007/02/25/using-dod-cac-and-smartcard-readers-on-linux/