I'll be happy to go in a little more detail, but let me say - I'm a beginner, not an expert at all, and other people here know better than me and make better stuff.
Second, check out here for tradtional costrel methods of construction and patterns: http://leatherworkingreverend.wordpress.com/the-reverend-hys-bigge-booke-of-leather/
What I did was take a 3" PVC pipe cap, and wet form some fairly thin veg-tan leather over it. I held it in place with a ratcheting metal pipe collar.
When the cap had dried, I trimmed it down to an even 1" edge.
I made a pattern out of paper for the body. I suppose I could have used high school geometry to figure out the circumference of a 3" diameter circle, but I use the prosaic method of a measuring tape.
The long edge of the pattern was the circumference of the circle, plus about 4" on top to cut and shape the spout and carrying-strap slots from.
I measured the paper pattern against the leather edge caps, and it all fit, so I cut it out of leather.
I marked the edges with a pricking wheel for where I was going to sew later.
I used that really strong rubber-cement type glue you can get at Tandy to glue it all together. I held it in place while it dried with clips from the office - those kinds with a metal body and little handles you fold back to open the clip? That kind.
Once it dried (I let it sit for a day) I pulled it out. Al Stohlman forgive me, but I used a Dremel to drill the holes where the pricking wheel had left marks, removing clips as I got to them.
I sewed everything together. I chose artificial sinew because I think it looks cool.
I got the mouth of the costrel wet so the leather would stretch, and put a 1" diameter dowel in while it dried. It took some work to get the dowel in there, but it's important that your spout be nicely formed and about the size to get a cork in to properly seal it.
When the leather had dried (about a day) I sealed it.
Now, I have found three methods for sealing leather vessels; brewer's pitch, wax and epoxy. Brewer's pitch on the inside and wax on the outside is traditional.
I personally prefer expoxy because it's easier and can be used for both hot and cold liquids. (within reason)
I do have an old crockpot full of beeswax, and I do sometimes use both wax and epoxy, especially if I've really botched the stitching and need to plug some holes.
With beeswax, get it just melted and not much hotter, or you'll cook the leather. Dip the leather until it stops bubbling, and then wipe off the excess wax.
Epoxy is much easier. I use Enviro-Tex lite, which is intended for food prep surfaces and non-toxic. Mix up about an ounce or two of expoxy.
Pour it in to your vessel, and put it on wax paper. The epoxy will flow to the bottom, so after about ten minutes turn it on its side, then repeat at every angle to get a nice even coating.
It takes about 8 hours to harden and 72 hours to completely cure. You can test waterproof properties after 8 hours, but if you see little puddles of expoxy on your wax paper, you'll know there were some holes.
No worries, it usually takes two or three coats anyway. The epoxy will eventually seep into all the pores of your leather, and color the exterior, too. I don't usually bother dyeing the leather - the picture above is uncolored, that's just the epoxy.
Important safety tip - don't put a cork in the mouth while there's epoxy drying!