Taqsim Study
Taqsim, Taqasim, Taksim - however you spell it, the meaning is the same. It is a section of a song where an instrument plays an improvised solo. How do you dance to it? That depends on the setting (recorded or live music) and the instrument. Listen carefully to what the instrument is expressing. The musician will use certain scales (maqamat) to convey different moods. Ultimately, you are free to "do what you feel" according to how the music moves you, but there are a few things to consider.
Dancing to a taqsim is more "internal", meaning you are expressing emotion & musical connection in your own little world. (By contrast, you are projecting outward with the entrance section of a song.) If you are performing to live music, the musician is really the focus of the taqsim, as it is his (or her) time to shine and your dancing shouldn't steal the spotlight.
In general, for wind instruments (nay & kawala) your movements will be more upward, drawn out, and extend into your arms, hands, even fingertips. Plucked string instruments, such as oud and qanoon, will bring out soft shimmies and small, round movements in the hips and chest. For instruments played with a bow, such as a violin, again your movements will be drawn out, but may remain more in the torso due to the tonal range of the instrument. (These suggestions are very elementary, of course the best way to learn is to work with your instructor and/or find a quality instructional DVD, such as Bellydance Taqasim - Improvisation Skills & Drills
Suggested tracks to learn more about the instruments (several come from the album: Egyptian Taqasim Vol.1
Nay by Mohamed Fouda 1
Cry to the Moon - Taqsim Nay
Kawala by Abdallah Helmy 1
Kanoun by Maged Naeem
Oud by Mamdouh El Gebaly 1
Oud Al Semai
Violin by Mohamed Aly 1
Cello by Emad Ashour 1
My taqsim playlist on YouTube. At this time it features musicians with their instruments, but I will add examples of dancers performing to taqsims, too.