bradgrafelman is right that you can get in a lot of trouble for violating a site's terms of service intentionally. It all depends on how much you might jeopardize their business model. Note that criminal charges may apply. I believe the FBI busted a bunch of ticket scalpers that had hacked together some scripts to auto-buy tickets off ticketmaster.
That said, you can set up a script to use curl to fetch the remote pages and configure curl to utilize a file for storage of cookies. Check out [man]curl_setopt[/man] and the options on that page you might be curious about are CURLOPT_COOKIESESSION, CURLOPT_COOKIE, CURLOPT_COOKIEFILE, CURLOPT_COOKIEJAR. The basic idea is to have subsequent requests to the site all use the same cookie file which is where session ids will get stored.
You'll still have to figure out where the login data gets posted, what the javascript does, how data is returned, etc. It's basically a bit of reverse engineering.