An email asking if I had anything on sharpening forstner bits prompted this shop tip. I did some searching online to see what was out there and was surprised to see that there was very little, and nothing that I would consider to be a cheap, easy and reliable method.
I had tried to sharpen a forstner bit before, but I used a mototool (Dremel) with a round grinding stone
and flat cutting disk, and pretty much butchered the bit with this combination. Part of the reason for selecting these tools was the assumption that the steel in these bits is as hard as the steel in a twist drill. It isn’t, and can be cut easily with a file. This is the case for the low cost bit used in this demonstration and a higher cost Freud set I have, but I can’t speak for every brand out there. Best to try it first, and if the file cuts, you won’t have any problem.
This method involves only two tools: a round chain saw sharpening file and a triangular file.

I start by clamping the bit in my vise using a pair of v-blocks to hold it securely, and begin working on the rim of the bit with the round file:

When doing this, I’m careful to pay attention to where the file is touching. You don’t want to wear down another sharp cutting edge while working on the rim.

After the edge is sharp all the way across, I sharpen the face of the tooth with the triangular file angle upwards:

The photo above on the right shows these two edges freshly sharpened. It’s important to evenly sharpen the edge along its entire length, and try to remove the same amount from both sides. This can be done by counting cutting strokes with the file.

Next is to sharpen the chippers in the centre. These angle up and all you need to do is rest the triangular file on this flat area and stroke upwards. Once again, it’s important to pay attention and not let the file contact another area that has already been sharpened. The geometry of these bits makes that fairly easy to do:

Two test holes in maple confirm the sharpening session was successful. Before this, the bit was dull enough to burn the wood going in.

Larger bits often have a toothed rim rather than a smooth one, but the same method is used for these. The rim is worked with the round file first, then the individual teeth are sharpened:

As with everything else, it takes some practice to become really efficient at this, but the payoff is big, if you use this type of bit often.

I made a video demonstrating the method: