Fiber-spinning spindles, both drop/suspended and supported, have many things in common and a few things specific to each type. Note I haven't made Turkish-style drop-spindles yet tho I have made a few Navaho-style supported spindles (a much larger version of the lap- or table-top supported spindles).
Will add more info here on each type and ways in which they're made. Unfortunately I'm not very good at using them since I don't knit (and thus don't have a use nor need for yarn). I do enjoy making the spindles used to create yarn, tho. :)