i do not understand or know the answer to this question: critically evaluate descartes methods in his meditation. are these methods the method of doubt and analysis? what are these methods? what is the lecturer looking for?
Sounds like you must have just been reading Descartes' Meditations on First Philosophy. Descartes writing is very interesting (and sometimes tricky) because it is often unclear exactly what he wants to accomplish with his writing. Add in the fact that he may have been obscuring certain points, or avoiding certain issues to avoid excommunication and persecution from the church, and it makes interpreting Descartes' philosophical work a bit of a challenge.
However, I think I can at least get you started with your question. It sounds like your lecturer wants to think about Descartes' unique method to finding out what is certain. The branch of philosophy concerned with what is true, certain, or counts as knowledge or belief is called epistemology, and Descartes is famous for his method of doubt. In his Meditations, he admits to being frustrated time and time again by finding out that something he thought was true was actually untrue, and thus desires to find at least one single thing that is undeniably and unshakably certain. He decides to doubt everything and anything that he thinks he could possibly be wrong about, until he reaches something that he believes must be true: that he is a thing that thinks.
In order to answer your lecturer's question, you might want to think about the following: is Descartes right to doubt everything that he does doubt? Is he thorough with his doubt? Or put differently, is he really calling everything into question? One of the most common objections to Descartes' "doubting" is that when he gets to the point where he admits that "there is thinking," or "there is a thing that thinks," he makes the unsupported jump to "I am the thing that thinks." Depending out how you view it, there could be a tremendous difference between admitting that thinking exists, and identifying yourself, most essentially, as that thinking thing.
Hopefully that gets you thinking and on the right track. You would do well to check out some articles about Descartes from actual scholars in the field, but if you don't have access to that, try some of the links below.
Stanford Encyclopedia of Philosophy entry on Descartes' Meditations: http://plato.stanford.edu/entries/descartes-works/#Med
Sparknotes entry for the Meditations (DON'T USE AS A SOURCE! But it's still helpful): http://www.sparknotes.com/philosophy/meditations/summary.html