I've made 3, son is a percussionist and played a bit when he was 16-18. Now he's moved on - orchestral percussion and timpani.
The cajon story:
First the theory - not much. Its said that it all derives from South America, warehouse workers making music on coffee bean cases. A cajon is just a resonant box. Unlike say a Timpani drum which must get a perfect note with the right harmonics, this is a basic un-tuned hand percussion instrument.
Snares - some have them, some don't. A footnote on snares at the end of this. If the box is to be played to accompany other instruments the snares might be more of a nuisance than a benefit, you want a box that can produce a range of uncomplicated tones.
Size - no magic formula, look up a few suppliers and see what they offer, needs to be a comfortable height for the user, I guess bigger is bassier, our #3 cajon makes a handy coffee table beside the sofa in the conservatory when not in use. 54cm x 30 x 30 worked, bigger player maybe taller to avoid knees-in-chin syndrome. Resonance hole in back, again not magic, about 1/3 of the way up, in my case 130 diameter based in the biggest hole saw I own.
Material and construction, this is where the 3 differed. First one proof of concept, quickly knocked together out of some rough old brown coloured ply I had in the garage (left by previous owner). About 15mm, with 3mm front panel. Made up the sides using battens at each joint, glued and screwed sides and back, more on front later. Took about an hour, looked awful sounded excellent!
So I thought, now to do it properly. 12mm birch faced ply sides, properly jointed, reinforced by chunky battens, 12mm inset back, 6mm ply front, looked brilliant but about as resonant as a wet cabbage. #2 has been cut up and the ply re-purposed!
Lesson, don't over think it, don't over engineer it, its a resonant box.
#3 is fine. 6mm birch faced ply - 4 sides held together with glued and screwed battens, 'butt jointed' but then ran the router along all edges to give that nice exposed edge ply scandi look. Back inset. Front was 6mm but still sounded a bit dead so went back to 3mm. FItted slightly oversized and trimmed with router. I reinforced around the resonance hole with a piece of thicker ply glued and screwed on the inside, you can carry it hand-in-hole, but its probably unnecessary to reinforce.
Notes about the front The front edge of the box needs to be square edged and unfinished for this to work. Then sand back the face of the top edge and top 1/3 of each side, half a mm will do. (so if you looked side on with it lying on a perfectly flat surface there would be a gap at the top). Screw the front panel (remember to countersink everything along the way) firmly to the edge along the bottom and 2/3 way up each side, no need to go ott, 2 screws at the bottom and 3 up each side is enough. For the top set of screws (top 1/3 of sides and a couple along the top edge) drill the panel slightly oversize so the screws don't bind. Then screw into edge.
If you do them up tight you have a solid thump, but if you back them off fractionally the player can rest palm on top of the box and get a 'slap' by playing the top edge with fingers as the face moves into the tiny gap your sanding has left behind. You can get a lot of different tones out - deep bass from ball of hand in middle of lower half, slaps and knuckles near the corners, fingers on top edge.....
Feet - needed to keep the box off the floor to get some resonance, carpet in particular kills it. Being a cheapskate I cut wine bottle corks on half and screwed/glued to the bottom. Keep them short, lots of players rock back onto back feet - you could use a batten along the back instead for a heavier player. Finish - its going to be carried about, sweated on, have beer spilled on it, so I used 2 thin coats of acrylic varnish. Probably best not to use any thick gloopy stuff. If the front panel is a bit rough you can get even more sounds out of it with scrapes and swooshes.
Snares - I fitted a set using guitar strings, from inside anchor to base a bit back from the front edge, fit a batten over them at the front edge, bring strings up and under a batten fitted to the top so they will lie against the back of the face, then bring them all to the back and design a tensioner of choice - I used hex socket bolts through the back. Not particularly effective and little used. If you really want a snare rattle maybe buy a snare wire set or if you know a drummer get an old stretched set when they are replaced. But before you do that think - is it what the musician wants? Snare wires can be inexpensive - about £5 from people like gear4music, typically 14" drum so overall length a bit more, can get 12, 13, 16s. You won't need to go to the ££££ concert snare versions....
Lots of word here - but remember the principal - its just a resonant box! Don't over engineer it.
Hope that helps