Install a current version of Net::Twitter. Versions earlier than 1.17 are not supported. If you are running 1.17, upgrade or apply this patch. If you don't have root access, you can still install the modules using this guide.
Create a directory for irssi scripts, if it doesn't already exist: mkdir ~/.irssi/scripts
Change to that directory: cd ~/.irssi/scripts
Remove any old version of the script: rm twirssi.pl
Download the latest version: wget http://twirssi.com/twirssi.pl
If you want it to automatically load with irssi, create an autorun dir: mkdir autorun
And create a symlink in it: ln -s ../twirssi.pl autorun

If you don't already have a twitter window, create a new window: /win new hidden
Name the new window: /win name twitter