How do we use the Present Perfect Tense?

This tense is called the Present Perfect tense. There is always a connection with the past and with the present.

We use the Present Perfect to talk about:

Present Perfect for experience

We often use the Present Perfect to talk about experience from the past. We are not interested in when you did something. We only want to know if you did it:

I have seen an alien.
He has lived in Bangkok.
Have you been there?
We have never eaten caviar.
past present future
!!!  
The action or state was in the past. In my head, I have a memory now.  
Connection with past: the event was in the past
Connection with present: in my head, now, I have a memory of the event; I know something about the event; I have experience of it

Present Perfect for change

We also use the Present Perfect to talk about a change, or new information:

I have bought a car.
past present future
- +  
Last week I didn't have a car. Now I have a car.  
John has broken his leg.
past present future
+ -  
Yesterday John had a good leg. Now he has a bad leg.  
Has the price gone up?
past present future
+ -  
Was the price $1.50 yesterday? Is the price $1.70 today?  
The police have arrested the killer.
past present future
- +  
Yesterday the killer was free. Now he is in prison.  
Connection with past: the past is the opposite of the present
Connection with present: the present is the opposite of the past
Americans do use the Present Perfect but less than British speakers. Americans often use the Past Simple tense instead. An American might say "Did you have lunch?", where a British person would say "Have you had lunch?"

Present Perfect for continuing situation

We often use the Present Perfect to talk about a continuing situation. This is a state that started in the past and continues in the present (and will probably continue into the future). This is a situation (not an action). We usually use for or since with this structure.

I have worked here since June.
He has been ill for 2 days.
How long have you known Tara (for)?
past present future
 
 
The situation started in the past. It continues up to now. (It will probably continue into the future.)
Connection with past: the situation started in the past.
Connection with present: the situation continues in the present.