WordPress.com has an included Contact Form feature that also works with self-hosted sites using Jetpack.

There’s an easy-to-use interface for creating forms. Some people may overlook a tab that lets you set the recipient email address and subject line for when the form is submitted.

If you go back later to edit your form, you’ll notice some code similar to this (for a default contact form):

Notice the additional code below (typed in green) that’s been added to designate the recipient and subject for a submitted form:

If you’re using the new WordPress.com page editor, the Contact Form button (to add or edit contact forms) is missing. So, instead, you’ll need to go to the Dashboard / Admin, then list all posts or pages, then edit the page using the old editor to have access to the easy Contact Form editing button.