First, make a script in PHP that reads the remote web site. Look into the fopen command. This will obtain all the HTML from the remote page and put it into a variable. Now you can look through that variable for the new content. If you know that the content is always in a certain place in the HTML, you will be able to use the ereg command to find the content which you will write to a text file or store in a database. Likewise, you will be able to use ereg to find the name of the new graphic that you want. You might have to make a system call from PHP to run wget to obtain the graphic. Save the graphic in some certain place on your server. This whole process is called "scraping" the other web site.
Call that script "obtain_data.php" or something like that. Test it a bunch of times to make sure that it is scraping correctly.
Once you have the script working the way you want it to, then you make a cron job that runs your script (obtain_data.php) once a day, every day at 3:00 am. (You don't want to run it at midnight because they might still be uploading their data. Give them a chance to get their content up). Cron is just a scheduler. Cron can run your script once a minute, once a day, once an hour, or even something fancy like "once every half hour from 5:00 am to 8:00 pm".
Now that your script is scraping the remote web site and storing the data, you need to modify your web site to read the data from your database and display the "borrowed" content and display an image tag that displays the new image that you have on your server.
This is an ambitious project because it will force you to learn fopen, wget, mysql, and regular expressions but it's a good project to know how to do.