Note: This tutorial deals primarily with non-paid Google Analytics analysis and optimization. However, much of what is discussed below can also be applied to AdWords or other paid campaigns.
But even if you take off your tinfoil hat long enough to get Google Analytics (GA) up and running on your site you still may not exactly understand the exact difference between a visit and a visitor. This techtorial aims to introduce you to some GA metrics that you may not be familiar with. You can then put this rarified knowledge to good use by thoroughly confusing your organization's stakeholders with weighty yet mysterious statistical terminology at the next staff meeting.
Let's begin by taking a look at a sample report home page -- the "dashboard" -- in Google Analytics.

Most of the metrics displayed on the dashboard are fairly self explanatory. It should come as little surprise that visits, pageviews, and pages per visit are all important statistics to consider when gauging the effectiveness of your site. (If you aren't familiar with these basic terms the Google Analytics Help Guide can help you get up to speed.) But let's look at two metrics that appear in the dashboard whose significance may not be readily apparent: bounce rate and average time on site.
According to mothership Google herself, bounce rate is "the percentage of single-page visits or visits in which the person left your site from the entrance (landing) page." So a bounce is tallied whenever a visitor comes to your site and then leaves without viewing anything else. Average time on site is just that: the average amount of time users spent on a site over a single session or "visit".
As opposed to more quantitative metrics such as visits and page views, bounce rate and average time on site provide important information for evaluating the qualitative aspects of a website's performance. A low bounce rate implies that people who visit your site are inspired to delve deeper in to it. A high average time on site indicates people are finding relevant content to view or interact with.
So what percentage could be considered a low bounce rate? And what's a good average time on site? These questions aren't easily answered and will vary for different individuals and sites. But GA's own benchmarking tool can provide some ballpark figures. (Note: GA's benchmarking tool is only available to sites that have it enabled. See "How do I enable benchmarking?" for more details.) To view the benchmarking overview select "Visitors → Benchmarking" from GA's main navigation list. By default you'll see a group of charts that compare stats from your site with other sites "of similar size." You can also set the topic area -- Religion, Finance, etc. -- of the sites to compare by selecting a category from the "Open category list" link.
Benchmarking in GA is still an imprecise science and, in my experience, works best with sites that have a significant amount of traffic. Nonetheless, if you want to compare your site's performance to similar sites then GA's benchmarking page is your best bet.
If you're more interested in comparing the performance of your site across two different time periods then Google Analytic's "Compare to Past" function will come in handy. You can find the compare to past option by expanding the date box located in the upper right of the GA interface.

Once you've entered a date range and clicked "Apply" you'll be able to view comparative charts and data for your site across the dates you selected. You can now either: 1) take credit for any increases in traffic or 2) find someone or something to blame for declining numbers.
Google Analytics provides website managers with a lot of raw data about their site's visitors and traffic. But how can you put all this information to good use? One way to do this would be to optimize your site's keywords toward bringing more high-value visitors to your website.
Keywords are terms that people have entered into a search engine to find your site. To view the keywords for your site click "Traffic Sources → Keywords". Here are a few key questions you'll want to ask when evaluating the effectiveness of your site's keywords:
If you want to take this a step further Google offers some great online tools that can help you get the most out of your keywords. A good place to start is Google's Keyword Tool, which can give you ideas for other keywords you might want to use on your site. You could also give Google's Website Optimizer a whirl. Website Optimizer allows you to dynamically change different aspects of your web pages -- such as headlines -- to see which configuration might prove most successful. Finally, if you have an advertising budget, you may want to consider investing a few dollars in Google AdWords. If you can afford it, AdWords offers the most reliable way to increase clickthroughs to your site using keywords. Visit the AdWords Beginner's Guide to learn more about AdWords and to get started using the service. Once you're up and running, here's a great tutorial about how to make the most of your AdWords which includes links to even more tools you can use to refine your keyword campaigns.
Of course statistics alone do not a successful website make. But combined with strong content and well-constructed pages, Google Analytics can help ensure you're casting your net as wide as possible across the 'Net. And until the Big Brother of Silicon Valley releases Google Hypnotize, Google Analytics will likely continue to be the best tool for finding new ways to get the right visitors to your website.
Resources
YouTube: Google Analytics Channel