Puncetto as it is commonly known today, has many other names, Punto Avorio being one of them. This needle lace is very attractive and though more commonly done in geometric designs, it can be used by the more advanced lacemaker to make curves. It is done in monochrome or even in bright multi-colours as on the traditional costumes of the Valsesia area in Italy.
If you've got access to Thérèse de Dillmont's Needlework Encyclopedia (also known as DMC's Complete Encyclopedia of Needlework), look under 'Needlemade laces' and check out the part on 'Knot Stitch Laces'. Look for Punto Avorio.
The best way to begin is to use the edge of a piece of fabric to attach to. Later you can try starting the way this lady does in her video.
There are a few books on this lace though all the ones I know of are in Italian and are difficult to find. Check out my library listing for titles relating to Puncetto. I have to admit to collecting everyone I have found so there are quite a few... to get you started I would say either the Manuale del puncetto valsesiano or the A scuola di Puncetto Valsesiano but if you are itching to give it a try right away, the Dillmont instructions are good or there are even some instructions in the Anchor Manual of Needlework under "Puncetto Work".
This is the corner of a fine linen handkerchief with Puncetto work that I purchased in Italy:
For free download of an Italian book from the early 20th century, go to Tuttoricamo, under the 'Books' section, then 'downloadable antique books', then under Amelia Brizzi Ramazzotti, click on the word 'Puncetto'.