Hi, Ziin. I agree with Marshall. 

Have done=PRESENT perfect. -->

----------Something in the past that still effects you to the current day. Going off Marshall's example: "I have traveled." Maybe your trip abroad went so well that it effects who you are today......maybe because of the friends you made; maybe the experience/work/job helped you gain the skills you have now......

----------Present perfect is also used when you want to mention something in the past WITHOUT mentioning WHEN. 

---------------Ex: "I have seen that movie before." / "I have traveled." 

Did=simple PAST tense. -->

----------Something in the past that doesn't effect you anymore. 

----------Simple past is used when you want to mention the past and WHEN it happened. 

---------------Ex: "I saw that movie YESTERDAY." / "LAST MONTH I traveled to America." 

Also, these tenses are great to know if you're interested in a job/an interview in America. 

Good luck with your studies! 

I would be interested in reading what other teachers have to say.   I think I might give this question a try, and maybe get some correction too. 

Have done 

did

These are two verb tenses. Have done is present perfect; thus would follow the rules and meaning of present perfect.  Did is past; also following the rules of past tense.

Past tense means: the action is completed, and normally at a specific time.  Present perfect means at some time in the past; also, the effect could be felt today.  Also, present perfect is used to indicate something done at some time in the past, in general.  I have traveled.  I have bicycled across the country. I have written a book.  Does that help? 

Your example: I did something. I have done something. This isn't enough for us to answer properly.  Think about writing something else and we can comment better.