There are a million tutorials on the ‘net on how to do this, but some folks at work mentioned they like the effect on occasion, and the way I do it is ever so slightly different than how others do it, and it’s a good opportunity for me to prove to myself that I’m getting the different layer modes.
We’ll start with this photo from our awesome cruise:

Open the file you want to de/re-colorize in the Gimp.
The first step is to add a new layer to the photo. Either click the New Layer button, right click in the Layers window and select New Layer, or just hit Ctrl+Shift+N. Give the layer a name like maybe B&W and make sure the Layer Fill Type is White.

Now, this adds a layer over the background, and the default mode for layers is “Normal” so it just covers your photo with white. We’ll change the mode of the layer so that it removes the Saturation - how much color shines through. When you select Saturation, then no color from the lower layer shines through, so it will appear black and white.

The next step is to apply a Layer Mask. If you learned anything from Custom QR Codes with the Gimp, you’ve learned that a Layer Mask is a part of the layer, which when turned black turns off part of the layer - allowing the underlying layer to just show through it - like a pinhole camera.
Right click on the Layer and select Add Layer Mask. PIck White for the color to initialize. This will set the mask to use the entire layer. We’ll color pieces of the mask black to colorize portions of the photo.

Now use the brush tool, and set the foreground color to black, and just draw over the parts of the photo you want in color.

Use progressively smaller brushes to get as detailed as you want in setting up the mask.
When you’re done, right click the mask and select Apply Layer Mask.
Like I said - this wasn’t the best photo for doing this. I’ve done others with flowers and such that work much more nicely.

Like these (Thanks Mrs. At Home:

