Is it your custom HTML form with custom controller for it and you just want to store the submitted data in Kentico Forms app? If so, then you'd need to:
Create a new Kentico form replicating the fields you want to store
Generate the code for this form object
In your custom controller form post action create a new form object, populate the fields and save
var form = new DancingGoatMvcContactUsNewItem
UserFirstName = "Firstname",
UserLastName = "Lastname",
UserEmail = "Email",
UserMessage = "My message"
Hope it will help!