Once you file your appeal request you will get confirmation from the Immigration Appeal Division that you have an appeal on record. That takes about a month. Then you will receive, within 120 days, your Appeal Record - which is, essentially, copies of your PR application and the CAIPS notes from your file. When you receive your appeal record you should retain an attorney to help you with the appeal. You may or may not receive a request from the IAD to provide "evidence and submissions" so that they can determine whether your case qualifies to be heard in an Alternative Dispute Resolution hearing. If your case is accepted into the ADR process, you should expect it to take another four months to get a scheduled hearing. If your appeal is allowed in the ADR process, the file goes back to the original visa office for reprocessing. There is no definite timeline for finalization - it seems to depend on each visa office. Even though allowed appeals are supposed to be given priority processing, that doesn't seem to be the case all the time.
My hubby filed his appeal request for our refused application back in January, we received confirmation in February, the appeal record 90 days later and a request for submissions and evidence due back to the IAD by June 4. We submitted that and heard nothing until last week - when we received notification that our case was being scheduled into the ADR process. We got our ADR date yesterday - scheduled for December 18. It'll be ten months from confirmation of our appeal request to the ADR hearing. If we fail at the ADR we will have the option to continue on to a full oral hearing - which can take another year or two - or withdraw our appeal. If we win our case goes back to the office that originally refused our file and it's anybody's guess how long it will take to be done.