One way is to fit the finished base to the horn by heating the horn and pressing the base in. Probably take two or three test fits, taking a little more off the base on the lathe as you go. On mine I usually have the base fit before any finish goes on it (May take a little more fitting) and the horn itself is finished when the base is fit.
Once you have it fitting and are ready to assemble heat the portion of the base that will go in the horn and rub some bees wax on it more is better, also heat the horn slightly and rub more bees wax inside it where the base will fit. Get both pieces warm, I use a hair dryer and push them together. With your third hand drill the first peg hole, I angle them slightly toward the neck of the horn, at 6 and tap in a peg, now 12, 3 and 9, all the while pressing the base in to the horn. You will have some excess wax to buff off, becomes part of the finish.
Now blow in it and see if it leaks, no leak good. If there is a leak heat the base and the horn where they come together and them blow in the horn, that should fill the leak with wax. If that doesn’t work find the leak by listening or light a candle and blow in the horn while rotating it close to the flame of a candle, that will pinpoint your leak. Slice off a t-h-i-n piece of wax and press it into the area where the leak is, now hit it with heat and press it in with your fingers along with a little more heat to work it into the crack.
If the initial fitting is done right there should be no leaks but Mr. Murphy has a way of getting his dues at times. Hope this helps. If it is not clear or I missed something just ask.
Tim C.