Custom pages with plugin

I’m developing some plugin where I would like to enable custom pages. In my case some custom page would contain a form like contact form (not literally). When user will fill out this form and send it, there should be the next step which will require more information. Lets say that the first page with form would be located at www.domain.tld/custom-page/ and after successful form submission, the user should be redirected to www.domain.tld/custom-page/second. Template with HTML elements and PHP code should be also custom.