MailChimp isn't the only email mailing list provider out there by any means, but it is the one that practically all the entrepreneurs I meet are using - probably because it's free up until 2,000 subscribers. So in this post I'll tell you how you can easily start collecting subscribers for your MailChimp email list. First, obviously, you'll need a MailChimp account. Click over to www.mailchimp.com and sign up for a free account; you'll need to click a button in an email to activate your account, and then fill in quite a lot of information before your account goes live - MailChimp needs your address in order for the emails you send to be compliant with spam prevention rules.
Then you need to create a list. Of course, there are many other customizations you'll want to make before actually sending out a newsletter, and you may also want to customize your signup forms and the confirmation emails your subscribers will receive (to do this, click the name of the list you've just created, then go to Settings > List Name & Defaults and click the "list forms designer" link next to "Send Final Welcome Email" - you can now choose from the dropdown menu which item you want to customise).
But you don't actually need to do anything else on the MailChimp site, if you don't want to, before you can begin collecting email addresses from your website visitors - it will work right away with the settings just as they are.
Next, you need to put a signup form on your site. You can embed a form directly into your web page using the code that they give you, but it's most likely you'll want to put the form in your sidebar, and for this you'll need a plugin. From within the admin area of your WordPress site, go to Plugins > Add New and search for "MailChimp." A list of plugins will appear, but the one you want is the one at the top of the list MailChimp List Subscribe Form by MailChimp and CrowdFavorite - this is the official plugin, and the easiest to configure (although, as you see, there are many others as well - go ahead and try out these ones out if you want to).
Once you have the plugin installed and activated, go to Settings > MailChimp Setup. Choose the list you've just created, and type the wording you want to appear on the form. You can also fiddle around with the appearance of the signup form, but you'll need to get it set up before you do this, so you can see how it looks. If you scroll a little further down the page, you can choose whether you want people to have to include their names when they sign up, or not - it's your call.
Now, go to Appearance > Widgets and drag the MailChimp Widget into the sidebar. You're all set to start collecting email addresses.