The Sefer Hasidim (Rabbi Yehuda Ha'hasid, Germany, d. 1217), in Siman 385 (listen to audio recording for precise citation), tells the story of an unmarried girl who did not wear makeup or jewelry. When she was told that this practice may lower her chances of finding a suitable mate, she replied that she has no reason for concern, as it is God who brings men and women together for marriage. (The Talmud indeed states that before a person's birth, God announces, so-to-speak, whom that child will eventually marry.) Sure enough, this girl ultimately married a pious Torah scholar.
This incident demonstrates the importance of God's role in the process of finding a spouse. It goes without saying that one must take personal responsibility and make every effort to find a suitable spouse, and the accepted practice is for young women to wear makeup, jewelry and nice clothing while dating. Still, one must recognize that this process is overseen by God, who ensures that everybody finds a worthy mate. Certainly a girl should not compromise her modesty to find a spouse.
Earlier (Siman 384), the Sefer Hasidim tells a different story, of a man who observed multiple fasts as a means of beseeching God to find his son a suitable bride, and the son indeed married and begot children. When the father's wife passed away, the son, as an expression of gratitude, observed no fewer than forty fasts to petition God to find his father a new wife. This demonstrates the importance of prayer as a crucial component of the process of finding a spouse for oneself and for others.
Among the Halachic questions that arise during the process of finding a spouse is the issue of testing for genetic disorders. Particularly among Ashkenazim, there are certain genetic features that are incompatible with one another, as the combination poses the risk of disease. Many young men and women therefore take a blood test in advance to determine their genetic compatibility. Are such tests permissible, or do they reflect an attempt to interfere with God's work in bringing people together, and to extend beyond the accepted range of human effort and initiative?
Rav Moshe Feinstein (Russia-New York, 1895-1986), in his work Iggerot Moshe (vol. 4, Eben Ha'ezer 10), writes that it is both permissible and proper to perform such tests, as part of one's efforts to ensure compatibility. Failing to perform these tests, he writes, would be akin to walking with one's eyes closed, without taking the precautions necessary to avoid injury and harm. Rav Moshe adds, however, that these tests should be conducted discretely in order to guarantee privacy and prevent stigmatizing and labeling should a defective gene be discovered.
Rav Shemuel Wosner (Israel, contemporary), in his work Shebet Ha'levi, likewise maintains that these tests should be encouraged, as they help prevent dangerous diseases, and that such measures are certainly within the domain of the efforts one should take to protect himself and his children.
Summary: It is important to recognize God's role in finding a suitable spouse for oneself or one's children, and therefore one's efforts in this regard must include spiritual efforts, such as praying and the like. At the same time, however, one must employ the natural means at his disposal in searching for a suitable mate, including testing for genetic compatibility to prevent the spread of genetic disorders.
