Each word might have different meanings depending on the context, but below are some common uses.
The word glide is similar to the word float. Something floating or gliding in the air.
Example: Can you see how well the frisbee glides through the air when you throw it?
http://www.youtube.com/watch?v=ayE_7oZhjuc. Watch this video of the frisbee gliding through the air.
Slide is commonly used for people or an object sliding on ice. Sliding is the motion that someone or an object makes as it move on the ice.
Example: Watch how well I can slide on the ice, I can slide far.
http://www.youtube.com/watch?v=OKKLdvA9Z54. Watch this video of cars sliding on the ice.
I think the word slip can be defined best by watching this video of people slipping on the ice. http://www.youtube.com/watch?v=Fbb3631ew_4.
Graze is the action that one object makes when it touches something just a little bit.
Example: If you throw a rock over the water, the rock grazes the top of the water.
http://www.youtube.com/watch?v=5uPATkNUb8I. Watch this video, how the rock grazes the top of the water.