Your complaint will be sent to the People Directorate Complaints Officer, who will then read it and decide what to do with it. The complaints officer will then write to you, and if there is to be an investigation into your complaint he will tell you who is investigating and how to contact them. The complaints officer will also let you know roughly how long he expects the investigation to take.
After your complaint is investigated, the person in charge of the investigation will write to you, explaining what they did to investigate your complaint and their findings.
The investigator will put at the bottom of the letter what the next steps are if you are unhappy with your complaint. Usually this will be to contact the Local Government Ombudsman.