How do I measure the effect of social media marketing on my business?

In general, try as much as possible to monitor the impact of socia on the fundamentals of your business.
It's always gratifying to see a large number of followers on Facebook or Twitter.
And in fact, this may be an encouraging sign.
However, if you are investing money and effort in social, you should expect more than just that.
You need to be able to measure the impact of social on business metrics like: new customers, brand recognition, sales, and so on.

If you are an internet based company, key measures could be the traffic / registrations / purchases generated from the social media.

Share of Voice compared to competitors.
Do you have more consumer engagement than your consumers? Social media can convert to measurable KPIs directly but is much more effective as a branding and customer service tool.

A good benchmark would be the uptake in audiences on the social channels themselves; measure the monthly increase in FB, Twitter, G+, LinkedIn followers as well as the number of conversations happening on FB and twitter.

This depends on many variations, such as: What is the goal behind your Campaign, do you want to increase your brand share, Awareness, fan acquisition, drive engagement , drive traffic to your website, ETC, also how many conversions you got ( Sales, Registration, Share, Subscription, Voting ,,, ) So, at first of all, you have to set your goals, then you should create a set of metrics to measure the effect of your SMM strategy.

I agree with what's been said and to monitor that you will need useful tools such as Google Analytics and Hootsuite.
The new Facebook Page Administration is cool as well.

By using the right platforms/tools that can measure conversion rates and successful campaigns.