On most of the originals I've inspected they used small pins - usually on the back side along the edges. Glue can also be used. On some originals I've also seen small teeth raised on the inside from the top opening using a a graver - when the throat or tip is pushed down onto the leather the teeth dig into the leather if you try to pull it back up.
As noted by crockett, at least by the 1820's the majority of Sheffield made sheaths were made of either paste board or papier mache with a thin veg/bark tanned leather cover (often bookbinding leather and the deco added was via bookbinder's methods including gold foil). Sometimes the sheaths were lined with velvet or wool baize (think pool table felt). I still haven't quite figured out how they did it although I've had a few sort of successes, by making the liner first and then gluing the paste board over that. Some sheaths of the period also had a flat spring inside for retention, most I've seen were on the full metal sheaths, but I have seen a few of the regular type with such springs.
Also the most common metal used by the Brits post 1820's was German Silver, brass generally denotes a US made product, but there are some exceptions to the rule.
One of the best resources I know of for looking at period sheaths of this type is Norm Flayderman's book, The Bowie Knife, Unsheathing an American Legend.
Hope that helps