I applied through the website for the EMEA AA3 graduate scheme. The process is standard for financial institutions. First step is to submit your CV, then to complete online tests (math, verbal, accounting, excel), then phone interview, and finally the AC.
Work on you accounting (financial ratios, balance sheet, cash flow etc.) and macroeconomics (interest rates, monetary policy, balance of payment etc.). Read thoroughly the methodologies online. Moody's AC is more competitive than usual, with a 5 to 1 ratio of offer holders.
HR could improve by reducing lag time between AC and offer (almost accepted another offer as I had to wait over one month to hear back, with no communication in between).