I'm currently applying for a job that asks for my Resume, a Cover Letter, writing samples (journalism job), and references. It is an online application, and there are only options to upload the first three of the required documents. I thought that the usual way to provide references was to list them in a separate document, but that is not possible here. I have also heard that you typically should not include them on your Resume, but I am not sure if this is true. What is the best way for me to provide references then out of these options?
You are correct that references should not be on a resume; keeping them in a separate document is correct. Contact the company and ask them how they would like to receive them. They should be able to point you to the correct online dropbox, an e-mail address, or some other place to submit them.
Within the online application site, there should be a "Contact Us" or "Help" button that you can use to talk to the right person. If this doesn't exist, look for an "About Us" or "Corporate Info" link at the bottom of the page and start by calling the company's general number, and ask for human resources.