The spec contains sample payloads for pretty much every resource. In fact, you can build a functional client for http-01 just by looking at the examples.

On top of that, if you're using a programming language that's at least close to mainstream, there's a very good chance someone has already written a library which handles most of the nitty-gritty details of ACME. As an example, this is all the code you need with the acme-client ruby gem in order to solve a http-01 challenge and get a cert (slightly abbreviated):

    require 'acme/client'
    client = Acme::Client.new(private_key: private_key, endpoint: endpoint)
    registration = client.register(contact: 'mailto:[email protected]')
    registration.agree_terms
    authorization = client.authorize(domain: 'example.org')
    # serve challenge.filename with content challenge.file_content
    challenge.request_verification
    # loop/sleep until challenge.verify_status == 'valid'
    csr = Acme::Client::CertificateRequest.new(names: ['example.org'])
    certificate = client.new_certificate(csr)
    # certificate.to_pem contains your signed cert. done!