It depends on where you are blogging. If you want a pretty easy method, just use Google's Blogger.com. You need to sign up for Google Analytics. Then you associate it with Blogger and can then track visitors.
Yes it also depends on the site builder you are using :wordpress, joomla etc.. some builders have a dedicated analytics page. Just sign up with google analytics and copy and paste the code into your site builder. it links your site automatically. you can check your traffic stats by logging in to googlle
If you are using wordpress, you will need to go in an change the template (all with in the wordpress control panel. Find the code for the footer and place your analytics code there.
For WordPress I highly recommend the plugin Ultimate Google Analytics. Works really well with WP and saves a lot of time. -M
you copy the little html code they give you and then put it between the head and body tags of your template