Breathe in through your mouth and pushing it down into your diaphragm.
Use the muscles of your stomach area to push the air out.
Start singing on a note about a fifth away from the highest point of your range. At a normal volume, slowly sing "hmmm" down a perfect fifth, blending the notes in between the top and bottom note to create a continuous sound. Continue to increase the pitch one half step at a time until you reach the highest note you can sing comfortably. This will increase your high range by lengthening and expanding your vocal cords over time.
Sing scales daily to increase your ability to sing in tune and expand your range. Start the scale at a low volume and end with the highest note of the scale with your loudest volume. Do not scream or overstress your vocal cords. Building strength in this way will take time.
Ensure that you are singing with proper diction. Poorly articulated words will sound muffled and weaker.