There are many different statistic counters about, some are built in with the web server provider, so check their first of all, if they do not offer a service, and the raw log files are not held on your web server I would suggest having a look at statcounter.com, you simply place some raw html code they give you onto your webpage and that is about it for the installation.They offer a free service which isn't bad at all and if you wish more details statistics, well then you have to pay for it. It is best NOT to show your users/customers how many visitors your website has had, as it is of really little use, it looks tacky. You don't see amazon or ebay showing you the number of visitors, so make sure your statcounter is invisible, you of course can always view the statistics via logging in but no-one else can.If your website is new after looking at your stats you might be rather disapointed at the lack of visitors, there are many reasons for this beyond the scope of this article but they include, your website not having good decent links and more importantly google has put you in its sandbox, this means that even though you appear in googles listings you rank very low until it is happy that you are proper genuine site (this is rumoured to last around 9 months)Statistics can be very useful, you can find out how people find you, what keywords you are doing well in, and how many more visitors you are getting month upon month, the number of users on the internet is still rising although slower now than it use to so make sure to keep this into account with the rise of visitors and obviously seasonal changes, depending on what your website is about.
Hope you don't get swamped by whatever statcounter you choose.