1. 忘记;遗忘
If you forget something or forget how to do something, you cannot think of it or think how to do it, although you knew it or knew how to do it in the past.
e.g. Sometimes I improvise and change the words because I forget them...
有时，我临场发挥改了词，因为我把原来的词给忘了。
e.g. She forgot where she left the car and it took us two days to find it.
她忘记把车子停在什么地方了，我们花了两天时间才找到。
2. 忘记;忘了(做)
If you forget something or forget to do it, you fail to think about it or fail to remember to do it, for example because you are thinking about other things.
e.g. She never forgets her daddy's birthday...
她从来不会忘记老爸的生日。
e.g. She forgot to lock her door one day and two men got in...
有一天她忘了锁门，两个男人溜了进来。
3. 忘记带;落下
If you forget something that you had intended to bring with you, you do not bring it because you did not think about it at the right time.
e.g. Once when we were going to Paris, I forgot my passport.
有一次我们准备去巴黎时，我忘了带护照。