The home for digital methods, as defined by Richard Rogers in his 2013 book, is the Digital Methods Initiative at the University of Amsterdam; its website homepage is here. The Initiative hosts two main projects: the first is the documentation for its annual summer school and the second is a course on digital methods, which you can find here. The course takes you through the basic components of the web: the link, the website, the engine, the spheres (a digital method for measuring and learning from the distance between sources on the Web), the webs, social networking sites and post-demographics, and Wikipedia and networked content. Each is discussed and there are tutorials on using methods to analyse their structure, as well as suggested readings. It's an excellent place to start if you are interested in digital methods.
There's also the Visual Social Media Lab, which hosts a number of projects experimenting with various methods for understanding how images work on social media.
Software for scraping images and/or text from social media platforms is diverse. Try these but explore further too
This blog post has some useful pointers about working with social media