There is a Coursera course here that goes through the basics of SNA such as network structures and measurements. They use Gephi in the course which is a common SNA software. (PS if you're not familiar with Coursera be aware that you don't have to pay for the course if you don't need to submit the assignments. Click Subscribe then under the button to pay there is a little link that says "You can also audit this course")
I got into SNA using UCINET and the book by the same team that made the software.
My current favorite SNA book is Social and Economic Networks by Matthew Jackson. It has a lot of math but is very comprehensive.
I know people use R for SNA but I don't have any first hand experience with that. Amazon has this book which seems to cover R specifically but I can't say if it is good or introductory.