Ok several options. Just execute a script look into rsh and rlogin which allow you to open a shell on another UNIX/Linux/Solaris/irix/hpux system.
If you have httpd (and php for php scripts) running on the remote server you could set up a web page with the cgi script (or php if installed) and show the results on in a browser.
If you need the script run regularly and the output available to review then on the remote server set up a script with cron (crontab) to generate your output and then pull it to your local server to evaluate with ftp or wget.