It all depends on how they've included the data within the PDF. Generally speaking, there's two possible scenarios here:
The data is just a text object within a PDF. You'll need to use a tool to extract the text from the PDF then insert it into your database.
The data is contained within form fields in a PDF. You'll need to use a tool to extract data from the form fields and insert it into your database.
Hopefully scenario #2 applies to you because this is precisely what PDF forms are designed for. Scenario #1 is really just a hack that you'd only use if you didn't have any other options. Extracting plain text from a PDF isn't as easy or accurate as you might expect.
If you're receiving a PDF form then all you need to do is match up the right fields in the PDF form with the corresponding fields in your database and then suck in the data. This process could be entirely automated if you wrote your own application.
Would this require writing an app or
is there an automated way of doing
this?
Yes, both of these options would require writing an app or buying an app. If you write your own app then you'll need to find a third-party PDF library that supports retrieving data from form fields or extracting text from a PDF.