了 does not equal to past tense in all cases, many native English speakers will be influenced by habitual thinkings of their mother tongue and make incorrect sentences. You'll be surprised to learn that, in effect, Chinese has no past tense grammar, "了" is just a modal particle indicating time sequences or conditions. But that goes too far away. Let's just talk about two most basic usages of 了, for now.
In this usage 了 is used in construction VERB+了. It implies a completion of an action. e.g. 我吃了一个苹果 - I ate an apple. When two or more verbs show up at the same time, put 了 behind the last one. e.g. 我起床刷了牙 - I got up and brushed my teeth. And when the sentence is in negative form which contains the character “没”, do remember that “了” mustn't be applied. e.g. “你没擦了黑板” is a wrong sentence.
In this usage 了 is placed behind the whole sentence. It indicates the consequence caused by a
previous incident. 他觉得不舒服，不能来上班了 - He feels uncomfortable and can't come to work. 了 implies the consequence caused by a previous incident - Because he feels uncomfortable(cause), so he can't come to work(result).
And occasions in which 了 can't be used:
e.g. 他前几天一直在复习了功课 - WRONG. Correction: 他前几天一直在复习功课。
e.g. 小王刚刚就在盼望了回家 - WRONG. Correction: 小王刚刚就在盼望着回家。
e.g. 你昨天应该完成它了 - WRONG. Correction: 你昨天应该完成它(You should finish it yesterday)。
e.g. 他们去年每周都去看了电影 - WRONG. Correction: 他们去年每周都去看电影
5.direct speech & narration
老师昨天说了：“记得做作业” - WRONG. 了 mustn't be applied after the verb "say" in a direct speech. Correction: 老师昨天说：“记得做作业”
老师昨天说(了)记得做作业。 RIGHT. 了 is optional here.
And you can look at this webpage for more advanced usages: