Modernly called a "drop spindle", a whorler (in period) simply consisted of a pointed, straight shaft (the spindle) inserted into a disk (the whorl).
Generally the whorl was near the bottom of the shaft, but there are "high-whorl" techniques, where the whorl is actually at the "top" end of the shaft, with the spun thread wound around the shaft underneath it.
This is much in contrast with a modern drop spindle which tend to also have a hook at the top end of the shaft - the thread is actually looped over this hook to help keep the holding loop from slipping off the spindle during spinning.
Also, methods of winding the thread onto the spindle seem to have evolved over time - early spindles all seem to have the thread wound "evenly" up the spindle - so that the lump of wound thread becomes "cigar-shaped". Modern drop-spindle techniques generally have the thread wound near the bottom (actually resting upon the whorl) and the thread forms a general cone-shape.
Period paintings of spinners often show the spindle being held by the right hand, with a distaff held under the left arm. In this way, the spinner was able to feed the fibre into the spindle between the two hands.