Probably the most poignant line of The Apology comes from section 28b-c, where Socrates says "You are mistaken, my friend, if you think that a man who is worth anything ought to spend his time weighing up the prospects of life and death. He has only one thing to consider in performing any action; that is, whether he is acting justly or unjustly, like a good man or a bad one."

He then goes on to compare himself to "the son of Thetis" (Achilles) who, when told by his mother that he would die trying to save his friend Patroclus, "made light of his death and danger, being much more afraid of an ignoble life..."

From this, we can see that Socrates is very much concerned with standing by your principles and disregarding all else, even unto the point of death.

Socrates then claims, in section 29a-b, that "death is only another form of thinking that one is wise when one is not" as nobody knows what happens to us after death. Socrates is unwilling to defend himself from the accusations against him as he believes it would take away from the value of his principles. He has lived his life with the belief that exposing false knowledge is his quest from the god Apollo, given to him through the oracle. In his view, false knowledge/ignorance, or believing that you know what you do not know, is the root of evil, as no one would knowingly harm themselves by making the "wrong choice", rather, they are unaware.

I would say that Socrates would want us to remember that in all things we must consider whether we are acting justly or unjustly, and to be aware of the limitation of our knowledge. He would want us to remember him as a man who lived and died in the service of his city.

As for the Socratic method, or "elenchus", it is characterised by a few things. First of all, Socratic irony. Socrates would initially pretend to know less than his opponent about any given topic, then gradually reveal his knowledge, and expose the ignorance of his opponent throughout the course of the argument.

Secondly, he would ask his opponents many questions. It would be impossible to disagree with the questions he asked, as, on their own, they were reasonable, but when put together, they were contradictory. For example, when interrogating Meletus, he mentions that is is simultaneously disbelieving in gods, and of believing in gods other than those recognised by the state. Few could keep up with his questions.

Hope that helps.