I did some searching on the web for a sort of construction manual, but found none per se. Instead, on the E-budo forums I found a bunch of threads by a German man named Sven Buelke who made his own very very nice fukuro shinai after contacting people like Dave Lowry (of Yagyu Shinkage ryu) and Dr. Karl Friday (of Kashima Shinto ryu) for the traditional method of making them. The information that Mr. Buelke presented was probably the best source for constructing them. Basically all the information I got came from Mr. Buelke's research and helpful posts.
You can head over to the e-budo.com forum, make an account, and search for "fukuro shinai" and you should find a ton of information on their construction. I'll present my own experience now.
Making them is not hard at all, it just takes (like many things) practice to make them look good. The most important things are the quality of the materials (you need durable, strong leather and sturdy bamboo that is not dry or cracked) and attention to detail while building the thing.
You'll need some basic tools, such as razor blades, scissors, a yard stick for cutting straight and measuring, stuff like that. Since cutting leather with a razor blade tends to pull the material, you can use one of those rotary blades that seamsters and tailors use if you want to spend the money: me, I just use the razor blade and cut slow and careful.
For your first couple prototype shinai, I suggest getting some cheap scraps of upholstery leather from a furniture store or off of e-bay (I got 10 lbs of leather scraps for 10 bucks plus 15 bucks shipping and handling - there's enough leather here to make about 15 fukuro!). This leather is thin and easy to work with to get the hang of making the fukuro, but later on, for more durable fukuro shinai, you should get thicker leather from a leather vendor.
A note on leather sizing: its thickness is measured in "ounces", which is the weight of a square foot of the stuff. Basically, every ounce is approx. 1/64th of an inch or 0.4mm in thickness. That upholstery leather is rather thin at only 2 or 3 ounces: for good durable fukuro shinai, Sven Buelke suggests cowhide or deerhide that is at least 1.5 mm thick or around 4 or 5 ounces. Deerhide is more abrasion resistant and durable than cowhide, but is more expensive. He suggests not using suede because suede is split leather, and therefore thinner and less durable, though it is less expensive. But IMO suede could work fine too, considering these things are just training tools meant to be replaced.
If you're crazy (and don't mind the ethics involved of kangaroo culling) you can get kangaroo leather, which is pretty much the toughest "normal" leather you can get, barring exotic stuff like stingray or elephant. (A stingray fukuro shinai would be kinda cool though, dontcha think? Hard to find a piece of stingray leather large enough though, and hides cost like 100 bucks for large ones). I personally stick with the cowhide: its durable enough, relatively cheap, and you can strengthen it later with shellac, polyurethane, or lacquer.
For a standard 40" long shinai, you'll need a piece of leather about 32" long (30" of blade length plus a few inches that'll get used up in lacing the tip/kissaki) by X inches wide, where X is the circumference of the WIDEST part of your bamboo (say 1.25" inch diameter yields a circum of approx 4") plus an extra inch for the overlapping region where you'll lace the thing. Bigger is generally safer, as it will accommodate more sizes of bamboo, and the fukuro doesn't have to be tight anyway. I generally get a piece of about 32" by 5.5" or even 6".
For the lacing, I cut my own lace out of the leather using two razor blades attached to either end of a chopstick, which gives me a lace of around the width of a quarter inch. This was Mr. Buelke's genius idea; there's a picture of his setup at the E-budo forums. You don't have to cut straight to make the lace either: you can cut it circles or whatever and the lace will be for all purposes straight because it is so flexible. If you're careful, you can cut out yards of lace from a piece of leather only 5" square. You can also just use sharp scissors and cut in a spiral pattern if you're careful in keeping the width the same. You'll need a lot of lace, at least 40" worth. Believe me, it sucks if you run out of lace early and haven't finished lacing up the fukuro.
For the handle wrap, I use a piece of leather around 3/4" to 1" wide by 42" long.
For actually constructing the thing, image google fukuro shinai and see how the things look. It'll give you insight on how the things are constructed. Without going into exhaustive detail, take your 32" by 5" piece of leather and cut slits for your lace down each long side, about a quarter of an inch of the edge. Basically cut slits just a little bigger than the width of your lace, parallel to the shorter side of the piece of leather. If you want to make a lot of work for yourself but make a better quality fukuro, place the slits every half an inch or so or even closer (lacing this thing up will take hours though). I'm a little lazy and placed them every inch. Be careful to make sure the corresponding slits on opposite sides are at the right spacing and will overlap perfectly: if you don't, the fukuro seam will twist all screwy once you lace it up. Also place slits on the top of the fukuro to make the tip, though I'm still working out how to place them so the tip doesn't look crappy.
Then fold the leather in half lengthwise so that the outside of the fukuro is on the inside, and start lacing up the top. Any hints on making lacing the tip would be appreciated :-). Mine still have visible stitches. At some point you'll turn the thing inside out and continue lacing on the outside: just look at pictures and you'll understand how to lace the fukuro. Have patience! It takes some time. If the tip of your leather lace is too soft and you find it hard to push it through the slots, I like to spread some Loctite or super glue on about half an inch of the end: when it hardens, it acts like a needle tip.
After you're done, you can attach the handle lace, though I'm still waiting for an answer on how it is traditionally attached. Either use hide glue as was suggested before, or cut slits in the end and lace it to the end seam using the fukuro lace.
At this point your fukuro is done and can be finished using coats of lacquer. I haven't done this yet myself, so any hints? Should one use shellac, wood finish, polyurethane, water soluble? Is there even a lacquer specific for leather?
Making the shinai is ridiculously easy compared to the fukuro, but you want to spend the time in finding good bamboo. Check out garden centers, nurseries, local bamboo suppliers, cut some green bamboo from a neighbor who gives you permission and let it dry, anything: you want a pole that you can cut out a 40" length that isn't dry or cracked, and has walls that are around 1/8 of an inch thick to a quarter inch. Too thin and the thing'll break: too thick and the thing'll hurt. Also, try to avoid poles that have bulging nodes: getting hit by one of those focuses the impact and can hurt.
To split the bamboo, take a medium sized kitchen knife you don't care about anymore and a rubber mallet. Bamboo WANTS to split longitudinally, so its very easy. Just lay the middle of the knife edge on the tip, bisecting it, and hammer it in carefully. It should go in with no real effort. Then you can continue to hammer the knife tip that is sticking out the other side and guide the handle down, and the split should continue easily. At the nodes, you'll have to hammer a little harder to break through, but it shouldn't be a problem. Just split slowly and carefully to prevent the crack spreading too far.
I like to split the bamboo into 4 pieces for 30" (3/4 of the length), then resplit those pieces into 8 pieces, but only halfway (20"), then resplit those pieces again into 16 pieces (being careful when hammering to not snap the pieces) to about 15". I haven't tried splitting again into 32 pieces because by that time the pieces were so thin I was afraid I'd snap them.
And thats basically it. I like to tie up the bamboo at the halfway point with dental floss to prevent the splits from spreading, but its unnecessary since the bamboo is replaceable. You can also sand the edges of the pieces and treat it with oil, like a kendo shinai, but since I can easily replace the bamboo when they break at almost no cost, I don't bother. One of the beauties of these things. :-)
At this point, just slide the fukuro over the shinai (hopefully you sized it so it'd fit!), then take the handle lace and tie it TIGHTLY to the handle, whiplash style. Take a look at pictures and you can figure out how to tie it on: basically wrap the lace around the handle, then tuck it under the lace and pull tight, and repeat.
And there you go. That's how I've been making my fukuro shinai: anybody else been constructing their own have hints or tips? i'm still trying to perfect them.