The Cadsoft Eagle schematic/PCB layout program is the favorite among the open source community. Because of that there are lots of component libraries available. While it is a commercial program, the company offers a freeware version which limits the PCB size and a maximum of 2 layers. However, it does have a steep learning curve.
If this steep leaning curve concerns you , as an alternative, I am reading good things about the DipTrace program.
Having just spent a considerable amount of time trying to learn the EAGLE PCB software, I’m very familiar with the available learning resources. I list below what I consider to be the most beneficial training videos and documents on the web.
There are two major program functions that need to be mastered, (1) schematic layout and, (2) board layout. There are many youtube videos that demonstrate these functions, however most are of dubious value. I consider the two best to cover these topics by Jeremy Blum: Schematic Layout Tutorial Video, and PCB Layout Tutorial Video.
Element 14 Cadsoft Webinar Video on board creation is also an excellent video.
The Dangerous Prototypes series of tutorials are helpful.
A German individual who conducts Eagle training has posted his Power Point Slides which are useful.
Update (7/6/2013): I just received the new book from Elektor, “Learning to Fly with Eagle“. In my opinion, the book is a good introduction to the Eagle software. It is up to date and covers most of the topics well (lacks library part creation). However, I find the above videos and websites are just as useful, if not better.