To use a hang glider, you must have it equipped in the 'Special' slot in your inventory. Then, when you are ready to glide, press the Special Item button (G) to take it out.
There is currently an exploit which let's players hang glide forever. This exploit can be seen here.
While the glider is out, any time you would fall, you slowly descend at an angle instead. Your movement speed is also increased by an amount corresponding to your skill ranks (See the table below). You can extend your flight time by pressing the spacebar to level out your descent, but this quickly depletes your stamina. However, descending for too long without leveling out will cause you to lose control, and spin to the ground in tight circles.
To maximize your gliding time, it is recommended that you briefly and rhythmically tap space just often enough to halt your descent, as there is a ~1 second delay before you descend again. Be careful to conserve enough stamina for the eventual descent, however, since if you run out of stamina at a great height you will very likely lose control before you've descended to the ground.
You can increase the bonus speed as you put more points into Hang Gliding.