There is an initial investigation at the site and examination of wreckage a while later to attempt to establish the cause. Various components are sent for metallurgical testing, electronics are examined for saved data, flight data recorders are downloaded and interpreted.
Where component failure is identified it may be subjected to further independent testing because in many cases involving scientific investigation the results are subject to interpretation by experts. Different experts may arrive at different conclusions despite being presented with essentially the same findings.
Then there is a need to determine whether any human factors are involved in maintenance or operation of the equipment.
Were there any other administrative failings that led to improper maintenance or other failings.
In every case where a problem is identified, individuals and organisations are offered the opportunity to respond and challenge or justify the findings. This may involve legal procedings through civil courts which are notoriously long winded affairs.
A final draft of the report is prepared and sent to all parties concerned for any final comments or challenges before publication.
A complex investigation being completed and a final report published can easily take four years, especially if several parties are extremely interested in avoiding any blame for an incident.
Although the civil investigation can take a long time, any criminal charges arising will generally take even longer, as that investigation is generally not allowed to proceed until the civil process has been exhausted.
Obviously the reason for all accident investigations is to improve safety and to prevent a recurrance. It is perfectly possible to issue orders grounding aircraft for urgent rectification work to be carried out well before any formal report is issued if the problem identified is serious enough.