Here's some of my notes: I use the mnemonic COVERU to remember the 6 main assertions: Completeness, cutOff, Valuation, Existence, Rights and obligations, and Understandability.
Completeness Procedures: Tracing and Analytical review (CAT)
Completeness is the concern when you are testing something that is more likely to be understated, like liabilities and expenses. So if I wanted to catch someone leaving out expenses to make their net income look better, then I would trace documents. I'd gather a sample of bills and see if they made it into the accounting system or if they were left out. A lot of times analytical procedures are used on expenses to see if certain costs are unusually high. For example, I might compare all the expense accounts to the last 3 years and then go inquire of management ie, “office supplies expense is unusually low this year – is there any reason for that?” They might have a good reason, like they changed to a cheaper supplier. Or, management might be surprised, in which case I would trace more documents in that expense category.
Existence Procedures: Confirmation, Observation/inspection, and Vouching (COVE)
Existence is the concern when you are testing something that is more likely to be overstated, like assets and revenues. So if I wanted to catch someone recording fake sales to make their net income look better, then I would vouch transactions. I'd select a sample of sales entered into the system and then see if they have the paper back up to prove that those sales actually happened, like sales order forms or cash deposits into the bank account. I might even sample some sales orders and contact the customer directly to see if they really placed that order for that amount on that date (confirmation). A good example of observation would be inventory observations – since inventory is an asset, it is at risk of being overstated.
I hope that helps?