Tap on the menu icon (three lines) in the upper-right corner.

Tap on Accounts or Contacts (depending on where the file is).

Search for the Account or Contact.

Tap on the Account or Contact.

Swipe to find the Files tab.

Tap Files.

Tap on the File you want to download.

Tap the ellipsis (three dots) in the upper-right corner.

Tap the Download icon.

The file will now be stored in the Files App on your iPhone.