One very important piece to remember is that your competitors will be engaging with their users in a digital environment. It's very important to analyze how they do this so you can leverage their success or learn from their failure.
Remember that social media is not a one-way broadcasting system. You will probably be able to see the difference in overall engagement between your competitors that are responding to their followers and fans vs. the ones that are not. Regardless of what your competitors are doing, you should always make it a point to engage with your social media audience by responding to mentions and direct messages on Twitter, replying to comments on your Facebook wall and Google+ posts, and replying to comments on posts within LinkedIn groups.
I utilize tools from Hubspot, Google Alerts, and my own eyes to monitor them accurately. I am of course a cheap skate or someone who doesn't invest in tools outside of the open source / free world. If I did end up doing this full time, I would grab Hubspot, Google Analytics premium, and probably something similar to Rival HQ where I could monitor statistics of my competitors.
Check out monitor backlinks if you are wondering where their backlinks occur from - I've found that super helpful.