You would ask someone to help you with your homework, or if you were really desperate you might "plead," with somebody to help you with your homework. "Beseech," is not a word that you are at all likely to hear in modern spoken English and you will seldom see it written down, either. It's the kind of word that you'd find in the works of Shakespeare. We don't use the word "pray," as a direct request to other people, very often either, really. We use it in the sense of either worshipping a God or in the sense that we really want something to happen or not happen. For example, you might say: "I pray to God that I will find somebody to help me with my homework." or "I pray that this exam will not be too hard." But you don't say to somebody else "I pray you."

Vicente, these are both pretty strong words to use if all you need is help with homework. Your usage of the words is correct, but no one would ever say that unless they were being sarcastic. You would beseech someone to save your daughter's life. Beseech is not used except in the gravest of situations. Pray is just slightly less grave. I pray for your safe return. I pray for world peace. You don't pray someone helps you with your homework - I guess unless, if you fail this class, you flunk out of college, return home a failure, are disowned by your family, and live an isolated desperate life as a pauper unless someone helps you with your homework.

"pray" and "beseech" are both pre-19th century archaisms for "ask." Are you using the works of Shakespeare as a basis for learning modern English?

Pray is still used in certain American legal documents Julie's answer is right on. Actually, all three answers are great.