1. Past simple / present perfect
Present perfect is used:
Past simple is used:
Actions that finished in a definite time in the past
I bought this car last week.   
To ask when? what time? Where?
They have arrived. ≠
When did they arrive?
An hour ago.
Actions which happened in an indefinite time in the past and with visible results in the present
I have lost my key. (I can’t find it now)
Have you seen Ann? (She is not here now)
To describe very recent actions
She has just moved to a larger flat.

2. Past simple / present perfect
Present perfect is used:
Past simple is used:
To talk about past states that cannot happen again
Shakespeare was a writer. He wrote plays and poems. (from 1564 to 1616)   
For actions which finished in the past, one after the other.
She lived in this house for ten years and then moved to another one. (sequence of past actions)
For actions which started in the past and continue in the present
She has lived in this flat since 2005.
She has lived there for three years.
(She still lives there!)
To describe experiences in our lifetime
Have you ever eaten Chinese food?
I have already eaten Chop Suey.
I haven’t eaten Japanese food yet.
(in your life until now)
≠ Did you eat Chinese food when you were in China? Yes, I did.
(specific time in the past)

3. Past simple / present perfect
Time expressions:
Time expressions:
Yesterday
last week (...)
six months ago
in 1975, at 3 o’clock
Just, recently
ever, never
already, yet
since, for
so far
how long