If you want to have a contact form, you need to add a block “Contact form”. Here you can write a title of this block (if needed), that will be displayed on the home page, e.g.: “Contact us”.
As a default content page, there is already a fixed Contact form. The content of this form you can change in your Shopify Admin. Simply click on Theme actions -> Edit languages -> Contact:
There is also an option that allows you to add additional content if you want to have some on the left side from the contact form. All you need is to select a page in the “Page content”.
How to add and edit a page you can read here
In our example, we have selected the page “About our store” and this is what we have got: