Experiencing noise nuisance can be frustrating and stressful. Complaints are usually treated as an environmental health matter, to be handled by your local authority. The police are usually only involved if the noise becomes a breach of the peace, or where threatening or violent behaviour is evident.
In the first instance, you could simply try talking to the person who's causing the noise nuisance. It could be that your neighbour is not aware that their loud music or barking dog is a problem.
If the issue persists, log as many details as possible, include times and dates (if recurring) and contact your local council from the below list: