It's probably, as bikeNomad says, some form submissions and some HTML scraping. You might need to use cookies, too, which is something LWP::UserAgent supports if you tell it to:

my $ua = new LWP::UserAgent;
$ua->cookie_jar(new HTTP::Cookies);
[download]

Once your program has "logged in" to Yahoo mail, you will get a cookie, not unlike PerlMonks. You can use this to access subsequent pages over a period of time. Although the Yahoo cookie seems to linger around for quite some time, they will ask for your password on a regular basis just to keep you honest, so always be on the lookout for that kind of stuff.

When it comes to parsing the page itself, you could either go with HTML::Parser, which is a fine tool indeed, but when it comes to cracking tables, HTML::TableExtract is much more powerful. Oddly enough, HTML::TableExtract was developed, apparently, to get data out of Yahoo's finance site. If you tell it the headers of the columns you want, TableExtract will give you an array back that contains the table data.

Maybe this should be Mail::Yahoo or something.