I’ve figured this out.
For others who couldn’t, here’s what you do:
1. Upload the file from within the entry form, and when you do, an upload window will appear. It should prompt to ask you where you want to place a link to the file within the entry. Select the field and upload the file.
2. When you return to the entry form, go to the field where the link to your file has been inserted. Edit the name of the link to your liking (it defaults to the file name).
3. Save or publish the entry
I wish the location and name of the uploaded file was actually in the EE database, and there was a tag that could be used to format the link to the file on the entry in the weblog. For example, in my entries I want to have supporting PDF files and I’d like to have that appear in the same spot on every entry (using the template for this). It would be nice to be able to add a PDF icon next to the link as well.