If you find a pattern in a book or a magazine, the rights to the design belong to the author of the work. You need their permission in order to copy or distribute it to others.

If you have woven or knit a pattern published in a book or magazine, it is ok to post a photo of your work. Acknowledge your sources and cite the reference information of the book or magazine you used. If you have knit, woven or made something, using your own creativity, you can distribute that design as your own. If you took a class and learned how to do something, please do give credit and mention who taught you the technique. If you have learned a technique and want to share it with others, do so in your own words, describing how you did it. Please don't copy lecture notes or other materials from classes.

In my opinion, a weaving draft such as one that is found in the well-known Davison book can be copied and used. This book is a compilation of weaving drafts collected from many weavers. Weaving drafts have been used for many centuries and are well known and recognized patterns. I don't think anyone can claim "ownership" of the draft. Many of the Davison drafts can also be found in other weaving pattern books. Similarly in knitting, a pattern for knitting a seed stitch or a cable swatch isn't a violation of a copyright. If you did use a book for the draft, then do cite the book, author, page and publisher.

How you use that weaving draft or knitting swatch to create your own unique work can be copyright. If you use a draft to create your own work, select particular yarns, colours, and design to weave a table runner or blanket or knit a sweater, then that design belongs to you. If you weave a towel using a complete pattern such as one found in Handwoven magazine, the ownership of that pattern for the towel belongs to the original maker of the design and the magazine that published it. The pattern should not be photocopied or republished without their permission.

The above is my interpretation of how copyright rules apply to handweaving. I could be wrong.

Here are some resources that give more detailed information on coypright issues.

Stolen Stitches
An article on ZDNet News about the Needlepoint industry and it's stance on copying cross-stitch designs.

Cross-Stitch and Copyright
Carol Todd, About.com's Cross-stitch Guide discusses the controversy of sharing copyright needlework patterns.

Copyright and Quilters
About.com's Quilting Guide, Susan Druding has an excellent FAQ list on Quilter's Copyrights. These can apply to other crafts as well.

Lost Quilt
Copyright infringement information from the Lost Quilt page.