I posted a detailed step-by-step explanation quite a few years back but I’ll be damned if I can find it now… currently funky ‘search’ function lists everything by “Anonymous.” Also… why are some many posts being repeated right now?
Anyways - measure your box and get the dimensions centered where you want your box. Maybe just take the box and mark around it. This would be a good time to check the depth of the box and the thickness of your tail. Take a little drill bit and drill a hole in each corner. Get yourself one of those nifty stainless steel rulers and position it so it is right on those corners you drilled. Tape the ruler down so it is on the outside of the box outline. This way, if your blade strays off course you won’t be slicing in to the bottom of your board outside the line. TAPE THE RULER DOWN SECURELY. With a box cutter, sharp knife, or even single edged razor blade make multiple light cuts - starting at each corner and cutting towards the center. Don’t try to cut all the way from corner to corner or you’ll likely cut past one of the corner holes and fuck things up.
OK - got one side cut through the glass? (It may take a lot of light cuts) Move the ruler to the other side and do the same thing. Remember… tape down the ruler on the outside of the box area, cut from each corner towards the middle of the line, then from the opposite corner to the middle. Now do the cross cuts at the ends. Be careful as you don’t have a lot of distance and those knives can go fast. Once you’ve done all sides, dig the blade under a corner of the glass and peel up the rectangular piece you’ve cut.
Now you’re looking at a nice clean rectangular section of the board with no glass, right? Time to get out a sharp wood chisel and start chiseling out foam and stringer. Try to punch directly down at the ends and then carve towards the ends from the middle. just take it slow and cut a little at a time. Keep punching out the ends where the stringer needs to be removed. KEEP AN EYE ON YOUR THICKNESS AS YOU GO.
You don’t want to go through your deck glass, OK?
Once you’ve chiseled out a relatively even depth, test fit your box. If all is well, mask off the outside of your hole, LEVEL THE TAIL of your board, remove any bridges across the top of the box, insert your favorite fin, mask everything off - the top of the box and the fin. Install that sucker with some medium catalyzed resin and a layer or two of glass inside the hole. Use the fin to make sure the box is vertically aligned - tape it from tip to rail on both sides to keep it vertical. Check it from the nose and the tail.
Once that resin kicks off, get out your grinder and remove all excess gunk. Scuff a football shaped area around the box and ‘Cap’ the box with a layer of glass that extends around the box. I’ve heard that you can get by without masking the top of the box slot but I do anyway. Once the cap is cured, feather it out.
Finish the board as usual. Believe me this works - I’ve done lots of boards this way before I got a router. The sharp corners of my box installations were practically my trademark.
And yes - make sure you know what kind of foam it is. Like the guy above said, epoxy is OK for urethane and EPS foams but polyester is only for urethane foam.