Hosted free counters are probably the simplest and easiest option for the non-technically inclined. All that is required is that you sign up at a counter service's site, then receive a segment of html code which you must insert into the page you want tracked. There's nothing more to it.

All hosted counters - more commonly known as "free web counters" - follow this basic idea. The html code they give contains a url to an image hosted on the counter company's site. When a web surfer hits your page, they load the counter's image embedded on the page from the counter company's site. When this happens, the counter registers a "hit", and may record some other information about the request, such as the type of web browser the user uses (Firefox, Internet Explorer or Safari, etc.).

Some take this a step further, and use javascript in the segment of html code given to you to record additional information that browsers would not normally send along with a request for an image. This information may include the HTTP_REFERER header (contains the URL from which a user clicked to your page) or things such as the window size of the user's browser. Javascript appends such information to the counter image url, for instance, if the counter image is normally located at:
http://www.webstat.net/counter.php?i=yourid
it changes it to:
http://www.webstat.net/counter.php?id=yourid
&screenheight=600&screenwidth=800&referer=www.google.com/search
This information would not normally be sent along with the request for the counter image by a web surfer's browser, so javascript sticks it in the url for the counter to record for your betterment.

In addition, though it is rare for free counters to offer this feature, some offer a counter image that is actually a one pixel by one pixel transparent gif file -- so that most users will have no idea of its existence on a web page. Some people prefer this setup. Other than the imperceptible presence of the image, there is nothing technically different about using a tiny transparent image to count users.

Sounds too easy, then huh?

Of course, there are some drawbacks to using a hosted counter.

Many free counters do not offer it, and it is considerably more difficult for novice users to count more than one page. You can count every page as if it were one page, and you can count only the front page, but counting every page is difficult. If you can find a service that offers it, they may require you to register and get a separate segment of html code for every page you want to count. If you have a large, constantly changing site, this may be an untenable pain.

Some of the website does however allow you to add your counter to multiple pages, and also get statistical data about the most popular pages etc. One of these websites is http://www.webstat.net and it is a free service!

That being said, for its ease-of-use, the hosted free counter service is probably the most popular method of hit counters.