There are at least two ways to cast on in Hairpin Lace. I prefer the method that I learned as a child, originally taught to my mother by her crafty friend Mrs. M. My preference comes not only from my having learned this method first, but also because I find that it results in a more finished-looking end loop.
Mrs. M\’s Hairpin Lace Cast On (YouTube)
Mrs. M’s Hairpin Lace Cast-on (click for mobile video)
The method more commonly found online begins with the loop of a slipknot being placed on a prong.
How to make the HPL stitch:
Hairpin Lace Stitch (click for mobile video)
I like to use my mother’s foil technique to store completed strips.
Hairpin Lace Strip Storage (YouTube)