Starting with the most simple, which is also the least customizable, do a search for "web page hit counter". You will find many links to free snippets of script that you include in your page's code. Those scripts connect to the provider of the counting service, which is where they keep track of your visitor count and feed the info back to your web page. Suggestions include StatCounter and OneStatFree.
You can get a little more complicated, and have a little more control over how everything looks, by hosting your own visitor counter program. If you are using a "shared" hosting service (i.e. you do not have your own web server computer), then your hosting service probably includes some sort of "stat counter" or "hit counter". You will find it by logging into your "dashboard" and enabling that service.
Many hosting providers give you access to the "log file" (the record of your visitors) associated with your hosting account, and that can be used, with a little more effort, to support programs like AWStats or OneStat. Those types of programs use a local database, like MySQL, SQLite or one of their own, and your log file to show you more detailed information about your visitors than the more simple solutions can.
Lastly, you can go wild and install a commercial solution, such as those available from WebTrends, ClickTracks or WebSideStory to do your "web analytics", which are much more detailed and MUCH more expensive than any of the previous suggestions.
To sum up, there are solutions for every level of expertise. Start with the simple ones and move up as needed.