Just print something back to the browser periodically while your script is running. Anything will do, even a single character. If you don't need feedback during the computation, use a single space so it will not occupy real estate in the browser window.

... code

$| = 1; # set autoflush
print "Content-type: text/html\n\n"; 

# simulate long running computation:
for (1..3600){
    sleep 1;
    # or do some processing

    # sends a single space to browser every 10 seconds
    unless ($_ % 10){ print ' ' }
}

... more code
[download]

Update: Set autoflush before doing this.

On the apache server, configure Timeout to be longer.

Client-side is up to the client I guess. In Firefox, go into about:config and filter on "timeout".