After the Jews were saved from the pursuing Egyptians through the splitting of the Red Sea, they sang a song (Shirah) of thanks to Hashem known as "Az Yashir." One of the phrases in this song includes the words "זה קלי ואנוהו," "this is my G-d and I will glorify Him" (שמות ט"ו:ב'). These words have many different interpretations and explanations, and several ideas can be derived from them.
The positioning of this phrase before the next phrase, which reads "אלקי אבי וארממנהו," "(this is) the G-d of my father and I will exalt Him" (שם), teaches us many things. Rashi (שם בד"ה זה) writes that even the most humble of people pointed with joy and exclaimed "this is Hashem." Rashi then adds (שם) that the non-Jewish maid servants saw more then of the glory of Hashem than certain prophets. This interpretation fits with the words of the Shirah, because the Shirah first states "This is my G-d" and then it refers to " the G-d of my father." The reason the Torah doesn't refer here only to the G-d of our fathers is that some of these people were the maidservants who did not have ancestors that believed in our G-d. This shows that even the maidservants saw the same vision as everyone else.
The Ohr HaChaim also learns something from the position of the words "זה קלי ואנוהו". He says that one should develop faith in Hashem from his personal experience before developing faith from what happened to our forefathers. This is also demonstrated at the beginning of the Shemoneh Esrei where we first say אלקינו"," "our G-d," and then we say "ואלקי אבותינו," "the G-d of our fathers." Some commentators write concerning the Shemoneh Esrei that we first call Hashem "our G-d" because we are obligated to serve Him to our fullest capability. But there is much about His ways that we can not understand. In response to this lack of clarity, we proclaim that he is also the G-d of our forefathers, and we have complete faith in the tradition they have transmitted. Similarly, the Jews sang Hashem's praises after witnessing the splitting of the sea by referring to Him as both their G-d and as the G-d of their fathers.
The Ramban (שם) remarks that this Posuk uses an abbreviated form of Hashem's name, unlike in most other places in the Torah. The shorter form sometimes indicates that the full degree of His greatness was hidden from the world due to man's shortcomings; the people were thus declaring that they will strive to honor and elevate man's perception of Hashem so that He will be recognized in His full glory as the master of the world. It is also possible to suggest that Hashem was going to split the sea in an even greater way, but when Bnai Yisrael complained, showing a lack of faith, the miracle was done in a more natural way by use of an easterly wind to split the sea. This more natural way that Hashem performed the miracle is indicated by the shorter version of Hashem's name in the Posuk.
The Gemara in Sotah (דף י"א:) states that because of the righteous women in that generation, Bnai Yisrael were redeemed from Egypt. The Gemara continues to say that Hashem performed many miracles for those women who had faith in Him and continued having children. The women would become pregnant and would remain in their houses so as not to be seen by an Egyptian. When it was time for them to give birth, they would have the child in the field, and leave him there. Hashem would then clean the baby, nourish it and care for it. When the Egyptians found out about the babies, and came to kill them, the ground swallowed them and saved them from certain death. After the Egyptians left, they would grow like grass from the field, and when they grew older, they returned in flocks to the houses of their parents. When Bnai Yisrael were crossing the sea, these people, who were cared for by Hashem at birth, were the first to say "This is my G-d." The same manifestation of Hashem's intervention that took place when they were babies was seen here and was recognized by these people. The word "זה," "this," is understood to refer to seeing something again that had been seen before. These people saw Hashem now as they did when He was caring for them.
The word "ואנוהו" also teaches us important principles. In the Gemara in Shabbos (דף קל"ג:), some learn that this word teaches us that we should emulate Hashem. Just like He is compassionate and merciful, so too we should be compassionate and merciful. But others learn from the word ואנוהו the notion of beauty, that one should endeavor to serve Hashem in a beautiful manner. Examples of this are by seeking a beautiful Sukkah, or a Lulav, or a Shofar, and so on. When Hashem was caring for the babies born in the field, He continued to care for them even after their birth. He cleaned them, washed them, and made them beautiful. The words זה קלי"" thus say "this is my G-d" who cared for me when I was born and ever since. The word ואנוהו"" is explained, as noted above, to represent beauty and the need to emulate Hashem. Just like Hashem did not hold back in caring for me, I will not hold back from doing His Mitzvos properly, and in as beautiful a way as possible.