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The most common method of measuring social media effectiveness is to track activity-based metrics for each channel such as likes on Facebook, followers on Twitter, etc. Many organizations benchmark these metrics against the comparable measures for their competitors. In addition, tracking the growth in these metrics per dollar spent on social media campaigns is a widely used approach to monitor the efficiency of your social media spending.
Less common, more difficult, but more telling is the tracking of leads for sales related social media efforts. Tracking leads from social media requires a combination of web analytics for monitoring the sources of your website traffic and sales conversions for e-commerce activity along with customer surveys or point-of-sale data capture in order to determine the source and sales conversions for your retail, phone or mail order sales. Despite, the additional effort and process required to get this data, the results will enable you to compare the cost of generating leads and sales via social media to your other advertising channels - ultimately enabling you to optimize your marketing spend in the best channels for your business.
Check out this infographic on measuring social media effectiveness.