Depends on the circumstances. When you say report, do you mean to the police? If so, an officer will contact you. If you have evidence, they will want to see it. They may also want a statement or video interview with you, if you're willing, or they may film you on body-camera when you meet them. Thy can come to the house or you can go the police station, or meet somewhere else entirely.
The police are suppose to take positive action. That doesn't necessarily mean arresting the person responsible (though that's usually what happens if an allegation of assault has been made), but it will mean that at the least the parties should be separated. The accused person will normally need to be interviewed about the offence, which can sometimes happen on a voluntary basis but more often happens after arrest.
In cases of DV, the police can pursue what is called a victimless prosecution, which means they can carry on with the investigation, and take it to court (if there is enough evidence), even if the victim doesn't want to co-operate. That decision will be up to the Crown Prosecution Service when the police present them with all the evidence.
There are also other options available, such as Domestic Violence Protection Notices/orders in which the police can insist the perpetrator stays away from the family home for a set period of time. Violating this is an offence in its own right.
If there are children involved, the police will also consider safeguarding steps, but unless they have reason to believe the victim will not or cannot take steps to protect the child, this should be seen very much as a supporting step, not a 'being dobbed into SS' step - it is meant to help.
Hope that answers some of your questions. I hope you are ok. 