The Blogger supplied "Contact Form" gadget provides a very basic form, with few options. There's not a lot to do or see.
With the Blogger "Contact Form" gadget, what you see is what you get.
You add the form to the blog, and you change the Title of the form.
Use is simple. You fill out the form, and Send. The content, once sent, can't be edited.
The reply address is whatever you entered, in the "Email" box.
If you are the owner of the blog, the message goes to you. If the blog has multiple administrators, Send a test message, and have everybody check their Inboxes. Find out who should expect to see Contact messages, and what email addresses are targeted.
If you test the form on your blog, when using a Blogger account based on a non GMail email address, you may not receive the test entry in your Inbox.
If you, as the blog owner, want a form with more options, or the ability to manage form recipients, you use a third party form. You can use Google Docs, and create a simple "Contact Me" form, in 15 minutes. A Google Docs created form can have multiple, designated recipients, and can be edited by the sender. The Docs based form entry goes into an online database, which can be accessible by designated recipients.
You can embed a Google Docs based form in a page or post - and you can create your page or post as a separate tab, in the blog - as I added my Blogger "Contact Me" form or alternately, my Expanded Followers gadget, to this blog.
What you see below is my demonstration Google Docs form, embedded using an IFrame. The IFrame code is provided with the form, which required a brief 10 minutes to create. When you create your form, hit "Send form", then "Embed", to get the code for your form. You can see my improved Contact form, in my page, "Contact Me, Improved".
<iframe src="https://docs.google.com/forms/d/1JvoY2yf5aTChnvXlCgGsUerSCtI7RHpRdkq5SPBPm90/viewform?embedded=true" width="700" height="800" frameborder="0" marginheight="0" marginwidth="0">Loading...</iframe>
There are various third party, non Google "Contact" form suppliers - some free, others not - some reliable and safe, others not. Be careful, if you decide to use a non Google, third party, product.