Here's a handy checklist for the ranks leading up to Eagle.
The troop has also prepared an advancement guidance document that should help describe and clarify some of the advancement requirements.
Rank advancement records are emailed to scouts and parents semi-regularly.
Blank advancement forms are available on the Forms and Templates page. A good listing of rank advancement and merit badges requirements.
The troop tracks advancements using Troopmaster software. The troop registrar gets information into Troopmaster by looking at (high resolution, well lit) photographs of the relevant signature pages of the scout book, and the physical Blue Cards for merit badges. You can interact directly with the registrar, or go through the scoutmaster. Books tend to get photographed at troop meetings in the weeks leading up to a Court of Honor.
It comes down to this:
Have an old Scout Book and Working With the New (2016) Advancement Requirements
Print this PDF out (double sided, it folds to make a booklet) and insert into your pre-2016 Scout Handbook. Info on the 2016 requirements changes can be found here.
Merit Badge Blue Cards: Blue cards: what are they? why do I need one? what do I do with it?
Available Merit Badge books and Merit Badge counselors are listed on the Members page (don't see that in the menu? Then you need to sign in.)