Take a photo of your subject from the front and from the side, using bright even light. It works best if the photos are taken in the same environment. 

I asked my subject to make a face as though he was blowing bubbles for extra realism. 

Open both photos in your photo editing software.

Crop and resize the images so they'll fit in your jar. The image height should be about 1/2" shorter than the height of the jar's viewing area. My final image ended up at 6" tall and 11" wide after cropping and resizing. Your height will vary depending on your jar size, but 11" wide is a good starting point since that's about what will fit on a sheet of standard printer paper.

Copy and paste the two images into the same file and align them so the eyes overlap with the profile image on top. 

In Photoshop, make a layer mask on the profile layer and use the gradient tool to make the layer blend slowly into transparency, revealing the straight-on photo underneath. 

Adjust the size and position as necessary so the corner of the profile eye aligns with the corner of the front-facing eye. 

Unlink the layer mask from the layer to move or adjust the transparency area, without moving the image.

Once you're happy with the alignment, copy the profile layer and mirror it to create the other side of the head. 

I used the rubber stamp tool to fill in any gaps in the chin or hair line. 

Print out the image and roll it into a cylinder to see if the illusion works. Mine took 2-3 iterations before I was happy with the layout and size.

Do a test fit in your jar to see how it looks. 

Trim the edges of the image and round the corners if desired to make it fit in the jar better. My jar has curved edges so this helped the image lay a little better in there.

Cut a 1/4" hole in the paper for the air bubbles to come through. Make this hole bigger than you think you need. We need a good amount of sealed laminate here -- if we poke holes through paper we'll get leaks, so this hole is necessary to give us a sealed bit of plastic between the lips so no water can get in.

Laminate the paper making sure there's a good 1/4" of sealed plastic on all edges. 

Trim the laminate and use a pin to poke a few holes in the mouth area, making sure not to puncture the paper. The water seal requires plastic-on-plastic to stay water tight. 

Test the fit. If all looks good, laminate it a second time just for good measure. Poke your pin holes in the mouth and trim the edges, making sure to leave about 1/4 of sealed plastic all the way around. 

I didn't seal it well enough the first time -- the second photo is the result. 

To cover up the big hole required for sealing, and for extra fun, I added a fake moustache. Glue this on with RTV silicone sealant so it stays on underwater.