Start an octave above middle C. While playing along with the piano, sing up to the highest pitch you can sing comfortably.
Count down seven half steps from your highest pitch. This pitch will be the pitch on which you start your exercises.
Sing the syllable "Gi" it sounds like "key" with a "G" sound instead of the "K" sound. Sing up each chromatic pitch until you have spanned a major third, or four half steps. Sing the top note three times, then descend to the starting pitch.
Continue this exercise until you can't sing any higher. Don't force your voice; you will naturally extend your range over time by performing this exercise slowly.
Take a 15-minute break and then attempt the exercise one more time. Repeat this exercise each day to extend your range to eventually sing high C.