"Aharon spoke all the words that Hashem had spoken to Moshe; and he performed the signs in the sight of the people. And the people believed, and they heard that Hashem had remembered the Children of Israel and the He saw their affliction, and they bowed their heads and prostrated themselves." (Shemos 4:30,31)
The flow of the pesukim would lead one to understand that the people believed in Hashem due to their seeing the signs/miracles that Aharon performed, i.e. the staff changing to a snake and then again back to a staff, the leprous and healed hand, and the water of Egypt turning to blood, caused the people to believe. The Medrash (Shemos Rabbah 5:13), however, has a very different understanding of the pesukim. If indeed their belief came as a result of the signs, it should not have said "the people believed", but rather "the people saw", since when we describe something as a belief we are referring to something one cannot see tangibly with his eyes. The Medrash therefore teaches that they believed in the message of Moshe, not the signs. They believed in the exact formula that was safeguarded by Serach bas Asher - that the redeemer would present the credentials of "pakod yifkod", that Hashem has not forgotten you. Why, then, were the signs/miracles presented before the people? The Yefei Toar on the Medrash suggests that it was a dress rehearsal which was preparing Aharon for his presentation before Pharoh.
The powerful message of this parsha is that faith does not only reflect the supernatural, rather it creates it.
The miracle of Chanukah came about only after the effort of the Jewish Nation and their unrelenting desire to utilize pure oil to consecrate the menorah caused Hashem to respond in kind. The Talmud (Chulin 91b) teaches that Yaakov was privileged to have his majestic dream of the ladder only after reaching Charan and realizing his failure to pray where his forefathers did, and began to retrace his steps; only then did he merit k'fitzat haderech, the miraculous contracting of the earth on his behalf. The daughter of Pharoh was determined to save baby Moshe, even though he was impossibly out of reach. She stretched out her hand, and Hashem miraculously extended it to reach Moshe. Man has to take the first step, and his belief triggers the Divine miraculous response. While winding the strap of the Tefillin shel yad around our finger like a wedding ring, we recite the passuk, "v'eirastich li b'emunah - I will betroth you to Me in faithfulness" (Hoshea 2:21-22). The Yalkut Shimoni (619) comments that we are redeemed from exile in the merit of our emunah. For example, we merited Divine inspiration and sang the shirah upon our deliverance at the Red Sea in the merit of the emunah we displayed during that episode.
The Chidushei Harim insightfully asks "why does the Torah introduce the shirah with "v'yaaminu b'Hashem - they believed in Hashem", when in reality they saw Hashem? They literally pointed with their finger and said, "zeh Keili v'anveihu - this is my God and I will glorify Him", so where was there room for belief? They saw/knew Hashem and were convinced of His control of nature and His mastery of the universe by the events they witnessed! The answer lies in the juxtaposition of "v'yaaminu" and "az yoshir". The passuk should have said, "az shar - then they sang", in the past tense; why does it instead say "az yoshir" in the future tense? The Talmud (Sanhedrin 91b) teaches that this is a source in the Torah for the belief in techiyas hameisim - the resurrection of the dead, because the passuk is telling us that Moshe will sing again in the future. While the Jews saw Hashem in all His might and glory at the splitting of the Red Sea, one thing they did not see was techiyas hameisim. A Jew cannot live without emunah, which is our constant connection to Hashem, and thus even at a moment of great revelation like krias Yam Suf we still needed to have belief in Hashem.
The first of the Aseres Hadibros, which explicitly includes the belief that Hashem took us out of Egypt, is understood by the Sefer Mitzvot Katan (by Rabbi Yaakov of Corbeil) to also include belief in Hashem as the future redeemer; just as He redeemed us from Egypt, so will He redeem us in the future. The requirement for our active belief is exemplified in the teaching (Sanhedrin 90a) that one who does not believe in techiyas hameisim will not be resurrected.
As we start anew Sefer Shemos, the book of our geulah/redemption, we are not only reading about our past, but also learning how to affect the forthcoming geulah. The Talmud (Sotah 11b) speaks of the incredible faith of the Jewish women in Egypt, cajoling their husbands to procreate and give rise to the next generation despite the horrific environment. Hashem responded in kind by miraculously preserving and tending to these children.
Let us realize the very special times in which we are living. If our tefillos are not as effective as we would like, perhaps it is because we do not really believe in their efficacy and power. May our emunah in Hashem, His Torah, His people, and His land, speedily have the meritorious effect described by the navi Hoshea, just as it has in the past (ma'aseh avos siman labonim).