Background:
This instructable is a direct implementation of the "Mitchell Doughnut" guitar speaker directivity modifier proposed by Jay Mitchell from The Gear Page discussion forum. The most relevant discussion can be found in the Speaker Directivity thread.

Purpose:
A typical guitar amplifier with a 12" speaker will seem to have accentuated higher frequencies when listening directly on-axis with the speaker cone. Listening to the speaker "off-axis" will have the converse effect. This phenomenon is commonly referred to as "speaker beaming". The directivity modifier is an attempt to mitigate this on-axis beaming effect without affecting the off-axis tone. Refer to the above gear page thread for background on the principles involved.

End Result:
A 3/4" foam "doughnut" that will be affixed behind the grill cloth in front of the speaker cone. See pics.

Materials:
-Guitar Amplifier (this projects specifies a 12" speaker)
-12"x12" polyurethane foam sheet
-Large sharp razor blade
-Ruler
-Sharpie
-3M Super 77 contact adhesive spray from Lowes (optional)
-Black Clothing Dye (optional)

Step 1: Foam Acquisition

Order a 12"x12"x3/4"polyurethane foam sheet with a #4 firmness rating.
These can be found for $5.72+ship - part#85735K72 from McMaster-Carr.
I ordered 4 sheets for good measure and the box arrived the next day!

It may be worthwhile to buy a few sheets of varying thickness or firmness to experiment with. Several people have reported positive results using #3 firmness foam. Using 1/2" thickness foam (McMaster #8643K511) may be better for use with thinner baffles. Note, the 1/2" foam is white in color, and you will probably want to dye it black before installation so that it will not be visible through the grill cloth. Black RIT Dye is likely available at your local supermarket.

Step 2: Marking

Remove the speaker baffle from your amplifier and measure the diameter of the baffle circle. (My Fender Blues Junior has a baffle opening of 10.5".) You are going to create a foam "doughnut" that will fit snugly inside the baffle, so the doughnut's outside must be the same diameter as the baffle.

Use a ruler to mark the center of the foam sheet and then begin to mark the foam at a half-diameter from the center until the marks form a dotted circle. Perhaps there is a more efficient way to draw a good circle, but this worked for me.

Then, using the same technique, create a smaller circle in the center with a diameter of 3" (1.5" radius).

Step 3: Cutting

Take the large razor blade and slowly begin to cut along the dotted lines. Try to make short half-stroke sawing cuts and slowly work your way around the foam. You shouldn't have to pinch the foam or press down hard with the blade. Let the razor do the cutting.

Step 4: Installation

When I created my doughnut, I happened to cut it just slightly larger than the baffle opening. When pressed it into the baffle, it fit very snugly and would require some serious pushing on the grill cloth to dislodge.

If your doughnut needs some assistance to stay in place, Jay recommends spraying one side of the doughnut with a light coat of 3M adhesive, and then applying the doughnut to the back of the grill cloth within about 30 seconds. This adhesive is weak enough to allow you to remove the foam in the future.

Step 5: Testing!

Reinstall everything in your amp/cabinet and grab your guitar. Try playing higher up the neck and compare the sound at different angles from the speaker. This crude testing should indicate that the on-axis sound of the speaker is much more comparable to the off-axis sound across the frequency spectrum.

Enjoy your beam-free amp!