There are several ways to integrate MailChimp into your WordPress website. Getting a form on your site is relatively easy. The challenging part can be to get it to integrate with the look and feel of your site, especially if you don't know anything about HTML or CSS. If that's the case, you may want to find someone to help you out.
Before we get into adding a form to your site, it is worth mentioning that you should only be collecting the very minimum amount of information that you require. An email address is essential for any kind of sign-up. If you want to personalize your mailings, you might request their name. I don't recommend going much beyond this or visitors may decide that it's not worth it or that they are being asked to share too much information.
Before you go any further, if you don’t already have a MailChimp account and at least one list setup, go through Step-by-Step to Your First Email Campaign first.
There are many MailChimp plugins available for WordPress. Some integrate pretty well into the look and feel of your site while others require some adjustments, usually to CSS code.
Some of the ones I've used on projects include the free version of the Nmedia MailChimp Widget. The MailChimp Widget and MailChimp List Subscribe_Form plugins seem to include good language support if you plan on installing it on a non-English language site. If language is an issue for you, you may need to try a few plugins before you find one that shows up in the right language and looks great.
Tip: The text that appears in your form may be controlled by the text that you typed in on the MailChimp site while others allow you to customize the text in the plugin's settings. The Nmedia MailChip Widget mentioned above, for example, reads the text from the MailChimp site when you first create the form. If you want to change the text in the form, you need to make the changes on the MailChimp site and then recreate the form in the Nmedia MailChimp Widget. Unfortunately it does not provide any other way to apply changes.
More information is available for MailChimp International Language Support on the MailChimp site.
Other CMS Plugins
If you are not using WordPress, take a look at the MailChimp Integration Directory to find a plugin compatible with your CMS, CRM, eCommerce or other type of site.
If you would rather not use a plugin, you have the option to embed HTML form code you create on the MailChimp website. You start by creating the sign-up form on the MailChimp site. When you are done, it will give you the HTML code to copy and paste into a widget or other content area on your site. You'll find a video tutorial and detailed instructions to follow on how to do this on the MailChimp Support site.
If all that seems too complicated, you can create a sign-up form on the MailChimp website and add a link on your website that says something like "Signup for my newsletter" which takes visitors to your signup form on the MailChimp site. However, I would recommend you try to keep it on your site in order to keep visitors on your site as long as possible.