I’ve recently been teaching someone to make lace and they were looking for a basic pattern to get going with. If like them you’ve just got started making lace (check out the two Getting Started tutorials here for some help and advice) here are a couple of patterns that I can recommend:
Fan pattern edging, p12, Pamela Nottingham- The Technique of Bobbin Lace
Fan and diamond sampler bookmark, p38, Pamela Nottingham- Bobbin Lace Making
Hearts edging, p40, Bridget M. Cook- The Torchon Lace Workbook (This book also has an excellent section of exercises to teach you new stitches)
but as they aren’t published in a book I can’t share them here. However there are plenty of resources out there so have a look round.
Don’t try anything too complex for your first piece though- it’s easy to get dazzled by the pretty patterns out there but over-stretching yourself and getting stuck is a a big step along the road to an abandoned project.
If you’re making an edging, I’ll be posting a tutorial soon on how to join lace neatly. Good luck with your makes in the meantime.