You register for the visa lottery online and you usually have to attach a digital photo of yourself. You will have to provide your name, date of birth, gender, country of birth, mailing address, your spouse' info, your children's info (especially under 21) your marital status, and a photo. You should send only one application per person otherwise they will disqualify you. But your spouse can send their own application as can your children if they were qualified to apply on their own notwithstanding applying for the lottery and can immigrate without you if need be.
You can apply on the Department of State website: www.state.gov (travel/business, Visas for Foreign Citizens, coming permanently to the U.S.)