Basically, the bird whistle produces sound by blowing air over a membrane. When you clamp the whistle between the tongue and the palate with some space in between to allow the air to run through and around it, you are already there!
Note: Keep the round, white, jagged part to the back (see image below)
When you push the whistle gently up to your palate, you blow & pronounce sounds like TSHHH.. as in the first part of words like Cheese, Champagne, Chocolate, Chips, or Cheers. The sound that follows is the start of all.
You will see that it is easy! Make moves with your mouth, lips, tongue, and try to talk like you normally do, but then with some pressed air to it. You will get more control over the bird whistle, and even your own voice and articulation.
Every bird has its particular sound. You can try to imitate some of them, but it is also fun just to whistle what you have in mind yourself. This is a whistle, and you are the bird. That's why you have your own specific sound.
Everything is possible, and you will do it without even thinking of it, like a new language, your second nature, free as a bird you are.