Q:

Recover metadata information from photo

Suppose a photo has been taken and the date was incorrect on the device.  Is there any way to correct the date on my computer after the fact?  Is it possible to find out the real date the photo was taken? Or will it just show the date the device was set to? For example, my photo says 2020 but was actually taken in 2015.

A:

The metadata stored in a photo for the "captured date" is only stored once in the file. If it's wrong, then, no, there's not a way to retrieve the "correct" date. In fact, because the camera's date was set to whatever it was, from the camera's point of view, the date captured stored in the metadata is correct.

A:

Is it possible to find out the real date the photo was taken? Or will
  it just show the date the device was set to?

No, at least not from the information in the image file. The image file only stores the time the camera wrote there - if the camera clock was wrong, the time in the file will be equally wrong. However, you may be able to find the real times if

a) the camera clock is working correctly (e.g. is not fast or slow), and
b) you did not change it manually later

In that case you can check the (incorrect) camera clock, and calculate its offset to the real time (e.g. it is 3 hours 2 minutes in the future), and add it to the time of each photo to get its real time. For example, a photo that says May 1, 15:23 is really from May 1, 12:21.
... which brings us to:

Is there any way to correct the date on my computer after the fact?

Yes, there is - you can edit the date information in the image file. All modern cameras store image metadata such as time of capture in a special section of the image file called Exif. There are tools to edit this Exif data.
For example, you can use the command line tool jhead.
To subtract 3 hours 2 minutes from the timestamp of a photo, use:
jhead -ta-03:02:00 image.jpg

There are many other tools to manipulate Exif data.

