Generally, employers will be notified of the complaint against them, and will have an opportunity to respond. After filing their response, some processes involve mediation, which can be mandatory or voluntary.
If mediation does not resolve the matter, then the next step is usually a hearing, which is similar to a trial. Some hearings may involve witnesses, while some may only involve documentary evidence. The overall time it takes from filing a complaint to its resolution depends largely on the specific administrative body involved and its own procedures.