You must first have a Requirement Specification document (spec). Without a spec there is no way for you to know if the delivered software is even remotely close to the client's request or expectation.
Review the spec looking for inconsistencies, conflicts, and individual features and behaviors that you can verify through testing. Inconsistencies and conflicts should raise an immediate red flag indicating that the delivered code is either incomplete or incorrect.
For each of the individual features and behaviors that you found, write a procedure that you can use to test each one. Once you have this list you can run your tests on the code to verify the accuracy of the results.
Now, how to charge for this: If you assume that a developer makes $80000 per year, then your hourly rate should be around $40/hr. You should be able to critically evaluate about 25 pages per hour. You should be able to write the testing procedure for one feature in about 30 minutes. Testing the feature by following your procedure is highly variable--some features may require you to wait while a timer counts down, etc. You won't know all the details for this until you have reviewed the spec, but you might want to estimate 1-2 hours per feature. A state-machine diagram is very useful in helping you determine how you can get to each feature. This will also help verify that you have performed a full coverage test of the software.