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One of the easiest ways to install Google Analytics on a WordPress blog is to use the Semiologic Google Analytics Plugin. You can find a post about how to install Google Analytics in by blog linked above.

My favorite feature of Google Analytics is the possibility to compare two different time frames. I use this to show progress to my advertisers - 30% increase in search engines traffic, 25% increase in page views, etc.
I am also trying to set up useful goal conversion reports, but nothing really cool so far. Looking forward to hearing some nice tips on that here.

Google have uploaded a boatload of very informative videos on youtube, great for beginners and experts alike. You really should be a pro after viewing these.

I’m no expert on Google Analytics but what I used to do was analyze my data quite thoroughly. I’d then understand where my traffic was coming from and then try to replicate it again. It’s also useful to see which keywords are bringing in the visitors from search engines so you can target specific keywords to bring more people to the site. One other useful feature is to see what page your visitors exited, and for how long they stayed before leaving. Tweak your content to offer them an incentive to stay longer or read more pages/posts.