JMR - Klout is an attempt at a metric, but it's a mixed bag. Here are some observations about why Klout scores rise and fall:
While Klout allows you to tie into multiple social accounts (Facebook, Twitter, LinkedIn, Pinterest, Instagram, Flickr, etc.), it primarily is driven by Twitter & Facebook.
Scores rise through a combination of # of followers/friends, overall frequency of activity, and how much you engage with other folks, particularly others with high Klout scores. In the past, it was relatively easy to game Klout simply by posting more, and by engaging a lot with others. This lead to a lot of blabbermouths getting high rankings. Klout has modified their algorithm to not support this kind of behavior as much, but it still is a factor.
When your tweets are getting retweeted frequently, this helps boost Klout score.
Same goes for likes and comments on facebook.
I guess I wouldn't advise focusing on boosting Klout scores so much as:
Identify the best platform(s) to reach your desired audience (i.e. if you blog about cute kitties, focus on Facebook or Pinterest). For me, that's Twitter & LinkedIn, so the fact Klout doesn't value LinkedIn as much and does love Facebook makes it less relevant.
Follow and/or connect with the most influential folks in your sector, as well as 2nd and 3rd tier folks. Don't worry if they don't follow you back, but do engage with them by responding, retweeting, etc.
Regularly post your own content, or good pieces by others. Others you have been engaging with will begin to follow your content, and retweet/like/share your posts.
Follow back those who follow you and/or accept friend requests. This is initially important to build an audience.
Post frequently and consistently (i.e. 5-7 days per week)
If you care about scores like Klout, the above behavior will help them rise.
p.s. A couple of other scores are PeerIndex and Kred. Both are similar to Klout, but emphasize different things (PeerIndex is twitter specific, and Kred appears to focus on topical expertise