The auxiliary word ‘了’ might be as comlicated as English particles (like 'up' or 'off'). Sometimes there're no written rules to tell you whether a '了' is necessary or not in the sentences. So my advice is to remember some typical examples and learn from original Chinese marterials.

Jmat has offered some idiomatic examples, and here's the systematic explanation from a dictionary:

1.verb+了=did/have done：孩子长大了/他哭了/老师走了/冬天来了/写完了

2.adj+了=became adj：奶奶的头发白了/爷爷老了，走不动了

3.肯定句+了：陈述事实，有时表示句子或半句话结束(to state a truth, sometimes for the end of the sentence or a pause) 放假了，我可以好好休息了。/起风了。

4.增强or表达某些情绪，辅助断句(to emphasize or express certain feelings; gramatically 了 helps to cut or end the sentence)：比赛结束了。(a little sad, maybe lost it)比赛结束了，我们回家吧！（merely stating the truth, or don't care about the result）/终于放假了，我可以天天睡懒觉了！/太好了！/太美了！/不早了，回去吧。/好了，别哭了，没事的。/你病了，明天别去上班了。

6.强调命令/劝阻语气when you command/stop sb, 了 makes you sound more intense：别 verb 了【别吵了！我要睡觉！ （have been annoyed for quite a while）别吵！我要睡觉！(you want to start to sleep so you ask for quiet)/别笑了！/别玩了，老师来了。】

P.S. If 了 is pronounced as 'liao', it's totoally a different word

That? ummmm.....no 

:D :D :D

Thank you for your help guys. I really appreciate it. :) I just made my account so I am really new to italki. Do you have any pointers on using the website for someone who just started?

What Cola said here reminded me of this one: ( Matthew, you can try this later ^_^ loll..)

题目：请解释下文中每个“意思”的意思。

阿呆给领导送红包时，两人的对话颇有意思。
领导：“你这是什么意思？”
阿呆：“没什么意思，意思意思。”
领导：“你这就不够意思了。”
阿呆：“小意思，小意思。”
领导：“你这人真有意思。”
阿呆：“其实也没有别的意思。”
领导：“那我就不好意思了。”
阿呆：“是我不好意思。”

I  can understand how complicated and confusing things about chinese are for you sometimes. The best suggestion I can give you is that use it in your daily life as much as possible and try to create a chinese-speaking environment for yourself, listen more, speak more, and always try to use it to achieve something, like, try to buy some food or asking for directions ..etc. It'll help really a lot. 

Of course wish you would never stay hungry and get lost, loll~~ Good luck !

You use it to describe when a situation has changed as a result of an action.

Ex.

下雨了 - It's raining (and it wasn't before).

我以前不会说汉语，但是现在我会说了 - I couldn't speak Chinese, but now I can.

我来中国了 - I came to China. ie. I wasn't in China, but now I am.

我今天没有课了 - I don't have any more classes today ie. I had classes today, but now I have none.

Some people say it indicates past tense. This isn't strictly true, but there are a lot of cases when that's how you would translate it. The most important thing to remember is that 了 indicates that something has changed as a result of an action, but it doesn't necessarily mean the action is past tense. “下雨了" is more like "It's started to rain and now it is raining" instead of "It rained".

I'm neither a native speaker nor a teacher, so take anything I've said with a grain of salt. Anyone is welcome to correct any mistakes I've made.