The recorder is a popular reedless woodwind instrument that provides an excellent introduction to making music for old and young alike. While learning the lower notes is fairly easy to do, getting the proper tone out of the higher notes can take practice and a slight shift in playing technique.
Sit (or stand) up straight, as the upper notes require more precise breath control. Hold the recorder as you would in playing the lower register, but ensure that your right-hand thumb is positioned below the the fourth and fifth fingerholes, as it will be an important anchoring device while playing the higher notes.
Play "D," the first high note, by covering the second fingerhole from the top (with the left hand) and by completely uncovering the thumbhole with your left thumb, and anchoring the recorder lightly with your right thumb underneath. If you are moving from middle "C" to "D," the transition is easy, as you simply remove the thumb covering the thumbhole for "C."
Move your left thumb slightly to the left (or below) the thumbhole until the thumbhole is open, or "cracked."
Play "E" by using the same fingering as the low "E" (top three fingers of left hand, followed by the top two fingers of the right hand), with the thumbhole cracked.
Keep the thumbhole cracked and raise the second finger of the right hand, adding the third finger of the right hand to play the upper "F," which is the same as the low "F" (but without the addition of the pinkie of the right hand). For "F-sharp" (F#), raise the first and third fingers of your right hand, depressing the second finger instead.
Keep the thumbhole pinched and remove the right-hand fingers entirely to play the upper "G," further removing the third finger for "A" (both of which otherwise utilize the same fingering as the lower versions of these notes).
Raise your left-hand third finger from where it rested for "G," and add the first three fingers of the right hand for "B-Flat." For "B," simply remove the third finger of the right hand.
Play high "D" by placing your fingers as you would for low "F," then remove the second finger of your left hand, keeping the thumbhole cracked.
Play high "E" by placing your fingers as you would for a low "F-Sharp," then remove the first finger of your left hand, keeping the thumbhole cracked.
Practice the transitions until they are smooth. Experiment with how much of the thumbhole you cover, as well as with how strongly you blow into the mouthpiece, until you can consistently achieve the higher notes with a nice, pure tone and without cracking.
Use your tongue to control your breath, either against the tip of the mouthpiece or against the roof of your mouth, as if you are saying "da." This is called "tonguing the notes" and helps you to clearly enunciate the notes and the spaces between them. This also helps you to blow more precisely.
Experiment with the size of the opening of the thumbhole on the upper notes until you find one that allows you to make the cleanest notes without cracking.
Every recorder is slightly different when it comes to achieving a pure upper-register tone, so experiment with your finger placement and technique to achieve the sound you want.