A website form feeds the same Leads pipeline your staff already work in — there is no separate inbox to remember to check.
Website ▸ Forms ▸ Create. A visitor's full name is always collected; you choose whether to also ask for email, phone, address, date of birth and a comment, and whether each is required.
Extra questions come from your Custom Lead Fields (Settings ▸ Marketing ▸ Custom Lead Fields), so a question you add there can be used on any form and shows up on the lead's profile.
A new Lead is created with the status you chose, assigned to whoever you nominated, and any follow-up automation that listens for new leads starts running.