To display a contact form (or any other kind of form), we use and recommend the free plugin Contact Form 7.
To install it from your WordPress back-end, go to
Plugins > Add New, then type
Contact Form 7 in the search field.
Once the search performed, click on the
Install Now link.
Contact menu will appear in your left WordPress back-end sidebar, where you will be able to create and manage your forms.
For more information on creating and managing your forms, please visit Contact Form 7 official website, where you will find all the necessary documentation.