The Ramban in his introduction to Parshas Vayishlach enumerates a number of lessons to be learned from the stories recounted in the parsha. "This parsha was written to publicize that Hashem saved His servant and redeemed him from a power mightier than him and sent an angel who rescued him. Additionally, it teaches us that Yaakov did not rely on his righteousness but rather attempted to save himself with all his resources ..." Rav Wolbe explains (Shiurei Chumash) that Hashem created the world in a way that it should run in accordance with the laws of nature. The Avos understood that if He so willed that the world operate in such a manner, they must act accordingly. Therefore, all their dealings with others were within the framework of these laws.
Yaakov didn't merely say, "Hashem you're in charge and please save us." He sent presents to his brother in an attempt to appease him, while preparing for war and the possibility that he might be overwhelmed and be forced to flee. He did everything in his power to save himself and his family, because he realized that it was incumbent upon him to do his share, and that this too is an aspect of avodas Hashem.
Toward the beginning of World War II, Rav Leib Malin urged all the bochurim in the Mirrer Yeshiva to flee to Japan despite the fact that there were many great people that were of a different opinion. Rav Yeruchom Levovitz had impressed upon him that one must not rely upon miracles, but rather do all possible to save oneself in a conventional manner. His advice was responsible for the survival of the Mirrer Yeshiva; all those who fled to Japan were saved from the horrors of the Holocaust.
Nevertheless, Yaakov also davened to Hashem to save him from his angry brother. His down to earth attempts to save his family were intertwined with a prayer to Hashem. Likewise, we find in Parshas Miketz, that Yaakov told his sons to prepare a present for the viceroy of Egypt in an attempt to appease him to free Shimon and Binyomin. He also added a prayer on their behalf: "And may Hashem grant you compassion" (Bereishis 43, 11). All one's endeavors must be complimented with a tefillah to Hashem. Even when one must take medication he is supposed to pray, "May it be [Your] will that this endeavor provide a cure for me" (Shulchan Aruch O.C. 230, 4).
Hashem created the world in a way that requires us to abide by the laws of nature. However, there is a danger that he who is successful in his endeavors might begin to think that it was his brains and brawn which brought him success. Although we must do all we can, we should not lose sight of Who really is in charge. We must also pray to Hashem to help us succeed, because hishtadlus and tefillah go hand in hand.