Visit https://docs.google.com/forms

Create a blank form and name it as Contact Me

Add description if needed. 

Add questions (Name, Email, Address, Phone etc.)

Select "Responses" at top click on the 3 dots ⋮ and select "Get email notifications of new responses

Select "Settings" at top and select "Responses" and make sure to turn off all the below

•  Collect email addresses

• Allow response editing

• REQUIRES SIGN-IN - Restrict to users in Steegle.com and its trusted organisations

• Restrict to users in _____.com and its trusted organisations

• Limit to 1 response

 Select the "Customise theme" option at first from the top right to change the font, colour to change as per your requirement.

In your Google Site editor mode go to insert menu and scroll down to select "Forms" 

Under the Forms options you should be able to see the newly created "Contact Me" form. Now select that form and click "Insert" to add form on your page.