The two pieces of bamboo you need, must fit snuggly inside each other, without too much force, otherwise the inner piece tends to split the outer piece. Also any that fit too loosely will be harder to block off holes later. You may find that by using different parts of the same length of bamboo, you can find an ideal thickness.
Step 2: Cutting
Cut a length of the wider piece of bamboo, about 120mm long (this measurement depends on the pitch that you want, see notes), and two lengths of the narrower bamboo about 15mm each in length. Then scrape away any contents so that the bamboo is nice and smooth on the inside (i usually find that another piece of split bamboo works well).
Step 3: Mouthpiece: part 1
Take one of the smaller lengths and using a knife, shave off one edge leaving a flat side. Be careful not to cut too close to the centre and risk going all the way through.
Step 4: Gluing
Take the two smaller pieces and fill with glue, so that the centres are completely airtight.
Step 5: Marking
Place the large piece and small flat-edged piece parallel, lining up their top edges and mark on the large one how far down the small piece comes. Where the mark was made, saw down into the bamboo until you have just penetrated the centre.
Step 6: Mouthpiece: part 2
Next, take a sharp knife, and cut towards and into the bamboo, where you made the saw cut, so that you end up with a notch cut away. You will want to make this notch about 15-20mm long, so that it cuts the air nicely when the whistle is blown into.