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.
A Contact menu will appear in your WordPress menu, 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.