了 is a very common and simple word in Chinese.We use it in many many different situations. Here are the examples. [读音 liǎo] 1.在动词后，与“不”、“得”连用，表示可能或不可能. uses after the word“不””得”to explain doing something is possible or not。 eg.看不了。 做得了 2.明白，知道。know clearly，understand. eg. 这件事我已经明了了。 [读音 le] 1. as you said, it is added to the end of a sentence to imply that it happened in the past . eg 我看过这本书了。 我上个月去了一趟北京。 2.用在句子末尾或句中停顿的地方，表示变化，表示出现新的情况。It is used in the mid or end of a sentence to show changes or something new accurs. eg.外面开始刮风了。 突然他沉默了，掉头就跑。 3.modal particle。(I'm going to talk about this a bit more) A.something is surely to happen. eg. 明天又是星期六了，不用上学了。Tomorrow is Saturday again, and I don't have to go to school. B.advise,dissuade eg. 别吵了！Stop the noise C.plaint，sigh with emotion eg. 别闹了，你当然可以告诉我，我是你最好的朋友。Come on, of course you can tell me. I'm your best friend. These are the most common ways of using 了. Anyway, there are so many usages in other different situations which are very hard to explain to a non-native speaker. But it does't matter at all.you don't have to know all usages of a word, neither do we native speakers. For instance, 我吃了饭了=我吃饭了=我吃过饭了=我吃过了=我吃了etc. These are all the same and common in our daily life. Just listen more and learn to speak and don't need to remember every grammer.To be honest,I don't know the whole grammer but I can also use my mother tongue well.It's called "语感" .(language sense)