Well, first the Petitioner (person filing for annulment) must fill out the paperwork, gather supporting documents (marriage record, divorce papers, police or counseling reports, Baptism certificates, etc.), and submit them to their Procurator-Advocate to be reviewed.
The Petitioner must also present the names and addresses of 3-5 Witnesses. Witnesses are people who knew the couple before and/or during the early portion of the marriage. If the Procurator-Advocate thinks the case has merit (grounds for annulment), the file is sent to the local marriage Tribunal.
The Tribunal reviews the case and decides it it does indeed have merit. If the Tribunal thinks there are grounds for annulment, they accept the case and notify the Petitioner by mail. In that mailing they send an additional questionnaire to be filled out and sent back. At that same time, the Tribunal sends a notification and questionnaire to the Respondent (ex spouse of the Petitioner) asking if he/she wants to participate and giving him/her a chance to tell their side of the story. The Tribunal also sends questionnaires to the Witnesses.
Ex-spouses have 30 days to respond. If they do not, they are sent another letter and given another 30 days. If they still fail to respond, the case proceeds. Witnesses are given, I believe, the same amount of time to respond. If not enough Witnesses send back their testimony, the case cannot proceed at that time. In those cases, the Petitioner must submit the names and addresses of new Witnesses or ask for an alternative if they have no one who could serve as Witness. This kind of thing is common for old marriages where the Petitioner cannot find people from that time of their lives, people they do find are unwilling to help, or their potential Witnesses have passed away.
Obviously, some ex-spouses are going to simply not respond and delay the case by 60 days plus mailing time. And, of course, not all Witnesses are going to actually fill out, notarize, and send back their questionnaires, further delaying the case.
Once all the questionnaires are returned the annulment case goes on to “trial”. A Defender of the Bond (job is to argue for the validity of the marriage) and Procurator-Advocate (job is to argue the marriage was invalid) review everything and write up statements. A judge reviews those statements and renders a decision.
If the decision is that the marriage was valid, the Petitioner can appeal. If the decision is that the marriage was invalid, the case goes to another Tribunal to be reviewed. If one tribunal says the marriage was valid and the other says the marriage was invalid, the case is kicked over to the Roman Rota for a final decision.
Now, there are literally hundreds and in some cases thousands of cases submitted to local Tribunals every year and each case must be carefully assembled and reviewed. In some cases, the Tribunal will interview participants in person or by phone in addition to their written testimony.
And the paperwork is quite extensive as the Church want a very clear picture of how the individuals who attempted marriage were raised, their understanding of marriage, their intentions at the time of marriage, and very intimate details of the married life the couple lived before divorce, etc… They want to make sure they understand, as best anyone outside a relationship can, what exactly happened so that they can render a decision according to Church law.
I am in the process as we speak and I was told my annulment case would take about 12-18 months to be processed as our Tribunal handles cases for parishes in 5 surrounding counties. They are also a bit understaffed. And we have it good here. We have a full time Tribunal staff. Some places, due to funding and availability of qualified people, have part-time staffs or have to send their cases to an out of state Tribunal.
Hope I helped you understand better why it takes so long.