A Head Boy badge is given to each Head Boy and Head Girl at the beginning of every year. These students are in their seventh year, and may have been prefects previously, although that isn't a requirement.
The badges are probably presented in a similar fashion to prefect badges, which is via owl post and included alongside a list of school supplies.
When Percy Weasley became Head Boy in 1993, his brothers Fred and George mocked him mercilessly, and even bewitched his badge to read "Bighead Boy".[1]