While forehands and backhands are the predominant throws with a frisbee, many more types of throws exist. Some of them even have weird names or descriptors. Throws like hammers, scoobers, pushes, thumbers, blades are some throws you might not be familiar with. The disc can also be forced to act certain ways. It can bounce or float, be thrown inside out or inverted, and even carry lots of "Zs" or rotations. Discs can also be thrown for rolling purposes or even to skip. Certainly many of these throws are unconventional or even trick throws so we should start with the basics.
A backhand and a forehand are the two main types of throws. A backhand is thrown by cupping your fingers under the rim of the disc with the thumb on top or the side. The throwing motion is closest to a backhand tennis shot. It should be coiled back across your body and with thrust and rotation smoothly let go in that tennis style keeping the disc rather parallel to the ground. It should be a fluid motion and may take some practice. The farther the disc is to be thrown, the more the outside edge of the disc should be tilted toward the ground. This is due to the gyroscopic forces that tend to "turn a disc over" with increased velocity and distance. The same would be true with the forehand. The forehand is typically gripped with two fingers under and thumb on top. The grip is different than the backhand in that the two fingers are aligned with the under lip of the disc and not wrapped perpendicular like a backhand. The way to throw the forehand is to try and "flick" the disc leaving your palms up at the end of the throw. This may seem unnatural at first, but be advised that the secret to throwing the forehand is in the flick of the wrist, not in the throwing arm motion like the backhand. The forehand usually takes much more patience and practice but once mastered it becomes second nature and allows for curving the disc by simple angle deviations.
Other throws sometimes are quite useful, but some are just for fun. A hammer or a bowl is a throw with the forehand grip that is released above your head at a slight angle. It is most similar to a football throw although obviously the grip is different. This disc gets high in the sky and curves back into whoever is catching it. If you throw it wrong it may look like a leaf falling from a tree in autumn. A blade is another throw like the hammer, except the idea is to get the disc high in the sky at a perfectly perpendicular angle with the ground. It is a difficult disc to catch and because of this it is used in various games like "Guts". A scoober is a throw with the forehand grip. It is a short throw normally that starts at your opposite ear in upside down position. It is released with the bottom side up and lazily curves a bit to the target. It is used in ultimate commonly when passing lanes are blocked. A thumber is like a forehand except your thumb is underneath the disc lip and your fingers are wrapped around the outside.
Still other variations and exceptions can be of use. A disc can be "bounced" where the disc is thrown toward the ground, but the rotation and angle of the disc allow it to bounce back up. In this way a disc might seem to float for a period of time with lots of spin on it. Freestylers often use this kind of throw to attempt all their tricks. The term "Zs" refers to the amount of spin you may have on the disc. The more "Zs" the more spin. Spin is beneficial because it can help stabilize a disc in wind. A push pass is not really gripped much at all. It is held lightly in a flat position and the disc is actually pushed by the outside lip usually ending up with very little spin and a wavering flight path. Still it is useful in some situations. Inside out throws or inverted throws are often used in ultimate. Forehands make right to left curving throws quite easy (for right handers). But an inside out forehand begins left and goes right. This is a much more difficult throw. Finally the skip throw is a fun one, but requires some skill. You can throw this with a forehand or backhand. For a right hander throwing a forehand, the outside edge must hit the ground at an angle allowing it to skip. If the disc hits anywhere else or is at a bad angle it won't work. With some work you should not only be able to skip it on concrete, but grass or any other surface.
I look at throwing a disc as a simple pleasure in life. For some strange reason there is certain amount of enjoyment that comes with being able to make a disc do what you want it to do. No longer are you swimming out to get your disc at the beach, or worse, apologizing to the lifeguard for nailing someone in the head. Sports such as ultimate rely on throwing skills. It does take some repetition, but once learned the analogy is similar to riding a bike. And after awhile throwing is something you don't even think about, it's just something you do. People will even look at you and say "How can you throw the disc like that?".