Orthodox Judaism presents itself as simply Judaism, the unbroken practice of the ages, requiring no founder and no founding date. That self-description is defensible about the content and misleading about the category, and both halves are worth stating.
The content really is old. Observance of the written and oral Torah as a single divinely given body, worked out through the Mishnah, the Talmud and the codes that follow from them, is continuous with rabbinic Judaism as it existed for well over a millennium before anybody used the word Orthodox.
The category is not old. Orthodoxy as a self-conscious movement is a nineteenth-century formation, and it exists because something appeared to define itself against. When Reform congregations in Germany began altering the liturgy, abandoning the dietary laws and treating ritual as historically conditioned, the traditionalists had to become a party, with spokesmen, institutions and a name. The name itself was originally an outsiders' label. Samson Raphael Hirsch in Frankfurt supplied the classic modern statement of the traditionalist case in the 1830s, and the slogan attributed to Moses Sofer of Pressburg, that innovation is forbidden by the Torah, is a deliberate polemical inversion of a legal formula and dates from the same struggle.
The defining doctrinal commitment is Torah min ha-Shamayim: that the Torah is from Heaven, given by God to Moses, and that the oral interpretation was given with it. That is what makes historical criticism of the biblical text unacceptable in principle to Orthodoxy, and it is the point on which it will not negotiate with Conservative Judaism, which grants the text a history, or with Reform, which grants the law no binding force.