This page lists descriptions of various spins and turns used in Middle Eastern dance and variations.
Stand in basic position facing forward. Now, pushing off with your left foot pivot on the right foot. Then step onto the left foot when you have made half a turn. If you exerted enough force you should end up facing the backward now.
Three Step Turn
Standing in basic position step out to the right with your right foot. Twist on that foot turning half way around to the right. Now step on the left foot and twist on it turning around to face the front again. Now step onto the right foot and then touch the ball of your left foot to the floor. When you touch your left foot you can do a hip lift or drop and the go back the other way. Your don't have to do a hip lift or drop you can choose to just touch the foot to the floor or you can even use another move here.
Basic Egyptian Turn
Start by stepping forward with your right foot and then bring your left foot forward, just touhing the ball of the foot to the floor and lift your hip forward by pushing against the floor. Step on to the left foot. Step with the left foot and then touch the ball of the right foot to the floor and lift the hip forward by pushing against the floor. Step on to the right foot. Now pivot either 1/2, 1/4 or 1/8 of the way around turning to your right (clockwise). Continue to repeat this sequence, step and touch and step and touch and pivot...
1/2 Airplane Turn
Stand in basic position. Just turn naturally however you feel comfortable or use the 1/2 turn or spin if it's easier. If you are turning clockwise (to the right) you will be using your left arm. If you are turning counter-clockwise you will be using your right arm. There are two ways to hold your arms, the first is to hold both up above your head in a soft "v", the second is to put whatever arm you are not using behind your head (like cupping the nape of your neck with your hand) and the other arm straight out from your side. Now you should start facing forward then turn 1/4 of the way around and drop your arm a little so it is at about a 45 degree angle from your body. Now turn another 1/4 of the way around and bring your arm back up to being straight out from your side. Turn 1/4 of the way around and lift your arm up so it's at a 180 degree angle from your body. Now turn another 1/4 of a turn and lower your arm back down to being straight out from your side. To make it simple your arm goes down in front and up in back, it's out to your side in between. Lean into the turns.
This is almost the same thing as the 1/2 airplane except you will use both arms in this when your arm is down in front your other one is up in back and so on. You should tilt your torso as opposed to moving your arms. Imagine imitating a plane (like when you were a kid) lean to which ever side's arm is down and straigten it up in between.
I can't really say that there's any specific way to spin, just do what comes natural when you spin. A tip for spining or turning of any kind is to use spoting. Pick a specific spot which you will look at while you spin, look at it as long as you can in the spin and when you have to, quickly turn your head so you can see it again.
A Turkish Woman and Her Slave by Jean-Etienne Liotard