GIMP Version: 2.8.14
Operating System: Windows
GIMP Experience: Basic Level

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Hello guys, I'm new to this forum and relatively new to photo editing (~2 years of experience and a couple of classes under my belt).
I have been attempting to remove the graininess from this photo and colorize it and I understand how to colorize it but I can't seem to even begin the process of removing the grain without losing the realism of the photo.

Could anyone point me to a guide that will help my situation or give me a tip on how to proceed? Thank you so much!

You could try - filter, enhance > symmetric nearest neighbour
Or gaussian blur at a very small amount.
Denoise will usually remove any details if they are small so I would use that only on a very large photo.

I made a QUICK TRY (about 3 to 5 min).
G'MIC has some useful filters on 'Repair'. Using layer Mask helps to choose the effects on the areas.
It didn't get bad.

But with patience and taking a few minutes to edit this image, possibly with a clone tool and / or healing tool and the result would be much better.

My "one-penny" attempt (Gimp only).

The image appears to be scanned at a very low resolution. I'd at least try scanning at a much higher resolution to see if that removes most of the pixelization.

Online coloring.

Interesting this new filter to auto-color black and white photos on PS.
https://youtu.be/Zx2xxCcnZNk

Years ago (2011) I had to retouche a few very old photographs. You can see the result here: http://dutchgimpers.nl/index.php/topic, ... l#msg10801. This is a photo of my great grandmother. There is a similar one on he same site of my great grandfather.

In the end I got some help of a russian guy. You will find a link to his blog: how to restore old photos. I have not tested the link, it is possible it doesnot exist anymore.

I agree with mahvin, If this was an image you scanned re-scan at a higher resolution and do not save in jpg format, save as a tiff or some other lossless format.