I am running 64-bit Fedora 10.

1)
sudo chmod +x /opt/cisco/vpn/bin/vpndownloader.sh

2)
I needed to download the 32-bit libraries from the repositories (all .i386 packages for the libs). You don’t need to download firefox 3, it’s just that it is packaged with almost all the 32-bit libraries that you need. You can get all the necessary files from the repositories.

These are the ones you need:
libnss3.so
libplc4.so
libnspr4.so
libsmime3.so
libsoftokn3.so
libnssdbm3.so
libfreebl3.so
libnssutil3.so
libplds4.so
libsqlite3.so

/lib and /usr/lib contain 32-bit libraries
/lib64 and /usr/lib64 contain 64-bit libraries

3)
Create symlinks to the appropriate libraries.
Here’s what /opt/cisco/vpn/lib looks like:
[... lib]$ ls -lAH
-rwxr-xr-x 1 root root 1149892 2009-07-13 08:35 libcrypto.so.0.9.8
lrwxrwxrwx 1 root root 22 2009-07-13 09:00 libfreebl3.so -> /usr/lib/libfreebl3.so
lrwxrwxrwx 1 root root 16 2009-07-13 09:02 libnspr4.so -> /lib/libnspr4.so
lrwxrwxrwx 1 root root 19 2009-07-13 08:56 libnss3.so -> /usr/lib/libnss3.so
lrwxrwxrwx 1 root root 22 2009-07-13 09:02 libnssdbm3.so -> /usr/lib/libnssdbm3.so
lrwxrwxrwx 1 root root 23 2009-07-13 09:02 libnssutil3.so -> /usr/lib/libnssutil3.so
lrwxrwxrwx 1 root root 15 2009-07-13 09:01 libplc4.so -> /lib/libplc4.so
lrwxrwxrwx 1 root root 16 2009-07-13 09:01 libplds4.so -> /lib/libplds4.so
lrwxrwxrwx 1 root root 21 2009-07-13 08:56 libsmime3.so -> /usr/lib/libsmime3.so
lrwxrwxrwx 1 root root 23 2009-07-13 08:56 libsoftokn3.so -> /usr/lib/libsoftokn3.so
lrwxrwxrwx 1 root root 28 2009-07-13 09:03 libsqlite3.so -> /usr/lib/libsqlite3.so.0.8.6
-rwxr-xr-x 1 root root 222300 2009-07-13 08:35 libssl.so.0.9.8

Then I created /usr/local/firefox directory and copied all files into that too (you can link there as well).

Last step for me was linking to the i386 version of zlib (libz.so):
sudo ln -s /lib/libz.so.1 /usr/lib/libz.so
sudo ln -s /lib/libz.so.1 /usr/local/firefox/libz.so

which enabled me to download the certificate from the VPN server.

Now I have Cisco AnyConnect Client 2.3.2016 working.