Theres a write up on composite bows in the bowyers bibles series of books in Vols 2 and 3 (Vol 3 discusses building a korean composite bow in some detail).
From what I've read they are a very involved build, with a construction time of in some cases over a year to allow the hide glue to fully cure deep within the sinew/wood/horn limbs.
I've never shot a true composite but I have a 45 lb samick SKB recurve which is the modern equivalent of the traditional korean bow, its fast, very fast the short limbs and deep recurving all increase the speed of the arrow send off, a true korean bow with its rigid siyahs would likley be even faster, a standard korean Archery range is around 161 yards.
You can buy a replica composite bow for around £100 - £200 but it will be a laminated fibre glass copy usually with a leather covering.
The following link has some great looking compsite bows with everything from the fibre glass replicas I've mentioned to true sinew/wood/horn composites (be warned they are extremely expensive £1500ish). theres also a good deal of information regarding the people who would have used the various styles of composite bows, Mongols, Turks, Scythians, etc, etc
http://www.grozerarchery.com
but if you've got the time and the determination then make youre own, once I've mastered making wooden bows I'll be trying a composite.
As Ranger Bob said
www.atarn.org is a very good source of information on them.
One more thing it is possible to make a hornless composite bow, I've got the article saved somewhere (it was on the primitive archer website) if your interested, but essentially the bow was made the same way as a regular composite but the limbs where deflexed then recurved instead of being reflexed and recurved, the deflex being to reduce the stress on the wooden belly of the bow. Aside from this the bows looked identical when braced to proper Composite bows.
Andy