I managed to find this. 1. Up and on; upward so as to get or be on: He climbed upon his horse and rode off. 2. In an elevated position on: There is a television antenna upon every house in the neighborhood. 3. In or into complete or approximate contact with, as an attacker or an important or pressing occasion: The enemy was upon us and our soldiers had little time to escape. The Christmas holiday will soon be upon us and we have hardly begun to buy gifts. The time to take action is upon us. 4. Immediately or very soon after: She went into mourning upon her husband's death. 5. On the occasion of: She was joyful upon seeing her child take his first steps. 6. On (in any of various senses, used as an equivalent of on with no added idea of ascent or elevation, and preferred in certain cases only for euphonic or metrical reasons): He swore upon his honor as a gentleman. You can use "within" with a time expression meaning "inside" or "inside the limit" - Within a week everything will be finished. "Within" also means: in the inner part; inwardly; internally Here are some additional examples: - within an hour, within reach, within limits - We must be back within three days. - He is no more within hearing.

Just forget about them, and when you next see them in a sentence, write down the sentence and understand them in context. Learn the entire sentence and its context. You should never learn any word in the abstract out of context. It ruins your English.

Your goal, as you implied, is to be able to use these words correctly. I doubt very much any learner would suddenly move from a state of ignorance to a state of proficiency simply by reading a list of definitions. Take for example this sentence, "Upon reflection, I yielded to the devil within." I don't think anyone learns to write it by reading a dictionary every day. There is no short cut. Learn each structured lesson in your textbook diligently. Find a good school. Asking questions such as "How do I use 'upon'?" is fun but it won't help you very much.

'Upon' means the same as 'on'. There are a few old-fashioned set phrases (such as 'Once upon a time' at the beginning of children's stories) where 'upon' is always used. But apart from these, you don't need to worry about it - just remember that it means 'on'. You will never need to use this word. 'Within' means the same as 'in' or 'inside' when you are talking about a place. As Sejo says, it is also used for a period of time. Here's a page with some translations for you : http://www.spanishdict.com/translate/within

there isn't really a grammatical rule to follow in this case, you see for such words you do need to memorize the context in which they are mentioned, i know it might sound bit a daunting but there's no other option.