Needle lace became popular in very late period, following on from the drawn thread work that was the earliest of laces.
Needle lace first made its appearance as the form punto in aria or "points in air" - named thus as it was a material constructed by string from "thin air" and adding bits until you had lace. This was opposed to the drawn thread work (or Reticella) in which you started from a material and removed bits.
Needle lace generally consists of having a strong edge secured on card or another stiff surface, and using a needle to delicately work many stitches over itself to create a worked area.
It is exceedingly time-consuming (the most time-consuming of all laces), and thus has always been incredibly expensive. Since every stitch is placed individually, there are absolutely no constraints on pattern, allowing for the finest and most complicated of filigree.
Only the most wealthy were able to afford needle lace in any quantity. The larger pieces (such as the Elizabethan ruffs) were often supplemented by cheaper and quicker bobbin lace edges. Some bobbin lace pieces even attempted mimicry of needle lace, with mixed success - there are some things that only needle lace can do.
One common form of needle lace was cutwork - used for household goods and clothing decoration in the 16th century. One form, known by the Italian name of reticella, was done by sewing a piece of linen to parchment with the lace patterns drawn on it. The threads were then drawn from the linen and embroidering the lace patterns in the open squares. Another form, known by the Italian name of punto in aria was done by embroidering the lace patterns on over drawings of them on parchment.
Here is a website with more information on cutwork: