How did the snake convince Chavah to contravene Hashem's command, bearing in mind His warning that they would die if they did?
Rashi: By pushing her against the tree and pointing out to her that nothing happened. 1 Rashi in Sanhedrin. (29a) adds that he did this following Chavah's statement that Hashem had commanded them not to touch the tree (even though He had not done so). 2
Targum Yonasan and Seforno 3 : He actually spoke Lashon ha'Ra (Motzi-Shem-Ra, to be precise), by claiming that they would not die, and that Hashem threatened them with death because 'every craftsman hates his rivals ' 4 - meaning that Hashem became all-powerful after eating from the Eitz ha'Da'as, and He did not want Adam and Chavah to become His rivals. 5
Many people believe that if Hashem does not strike them down immediately after sinning, it means that they have gotten away with it (because either Hashem does not know or He does not care). As we explained in the previous Pesukim, it is the way of the Yeitzer ha'Ra to create fantasies, to make people believe what is not really true. Moshav Zekenim and Chizkuni ask, what was the snake's proof? Even for eating, Hashem said that they will die that day, but not necessarily immediately! They answer that he told her that she will not lose through eating, for she is already liable for touching. Riva answers that she thought that death would come immediately. Moshav Zekenim asks that she was forced to touch. We cannot learn from this that there is no Misah for Mezid!
This gave the snake the opportunity that he wanted, and he said to her that, just as she did not die by touching the tree, so too, would she not die by eating it. Midrash Rabah (Bamidbar 19:2) says that the snake is found between fences, for it breached the fence of the world. I.e. it succeeded to entice Chavah to eat only after it made her breach the fence not to touch (Divrei Eliyahu on Bereishis 3:3).
As we see in the following Pasuk.
This is nothing short of blasphemy, since it denies that Hashem preceded the world and created it (including the Tree), besides ascribing human shortcomings (jealousy) to Hashem Kevayachol.
רש"י: דחפה עד שנגעה בו: מנין למדו זאת?
גור אריה: שאם לא כן, מנין לנחש לומר בודאות "לא מות תמותון"?!
רש"י: אמר לה כשם שאין מיתה בנגיעה: קשה שה' אמר שימותו ביום אכלם מהעץ, ושמא ימותו בהמשך היום?
גור אריה: האשה סברה שהעץ נאסר להם לטובתם מפני שהוא ממית, ולכן חשבה שאמנם תמות רק בסוף היום אבל היה לה להרגיש כאב מיד.
רש"י: אמר לה כשם שאין מיתה בנגיעה: קשה שהיא הייתה אנוסה בנגיעה בעץ [שהרי הנחש דחפה], ומנין לומר שכשם שאין עונש באונס כך אין עונש ברצון?
גור אריה: האשה סברה שהעץ נאסר להם לטובתם מפני שהוא ממית, ולכן חשבה שאין הבדל בין נגיעה באונס לאכילה ברצון.