The differences in the manner in which Reform and Orthodox Jews practice their tradition is grounded in their view of the Hebrew Scripture (Bible) and the status of other sacred texts, such as the Mishnah and Talmud. There are also law codes, such as the Mishneh Torah (by Moses Maimonides) and the Shulchan Arukh (by Joseph Caro) which guide the life of Orthodox Jews. For Orthodox Jews, the Hebrew Scriptures is a divinely-authored text and therefore every commandment contained therein must be obeyed. The Mishnah and Talmud are considered to have virtually the same status and are called Oral Torah. Reform Jews, however, understand the texts to have been written by human beings -- our ancestors. In my personal opinion, the texts are certainly divinely inspired and reflect our ancestors' best understanding of God and their covenant with God, as well as their view of God's will, but that is not the same as being divinely-authored. Hence, Reform Jews read the texts through the spectacles not only of a religious person, but those of the scholar as well. Some institutions are considered to be a product of the cultural milieu and societal norms of the ancient Near East when the Hebrew Scriptures were written down, and do not speak to our lives today. In addition, Reform Jews do not ascribe to the Mishnah and Talmud the same authority which Orthodox Jews do. While the Talmud and law codes guide the lives of Orthodox Jews, it is more accurate to say that they inform the lives of Reform Jews.
These differences in perspective can be seen in every aspect of life: how holy days and festivals are celebrated, how kashrut (the laws of keeping kosher) are kept, how the prayer service is organized and conducted, etc. But it is not accurate to generalize and say "All Orthodox Jews do this..." or "All Reform Jews do that..."
To learn more about the Orthodox perspective, I recommend to you the books of Rabbi Maurice Lamm and Rabbi Hayim Halevy Donin. To learn about the Reform perspective, I recommend the following books published by the Central Conference of American Rabbis: Gates of Mitzvah (life cycle), Gates of Shabbat (observing the sabbath), Gates of the Seasons (holy days and festivals).
In addition, if you are interested in the perspective of the Conservative Movement on these same issues, I recommend Rabbi Isaac Klein's A Guide to Jewish Religious Practice.