Present Perfect

We use the Present Perfect to talk about something that started in the past and is connected to the present.

He's had nothing but problems with his new car. (he had problems in the past and continues to have them)

That architect has designed all kinds of buildings. (the architect has designed buildings in the past and continues to design them)

We can use it to talk about something that happened at an unspecified point in the past(we don't know when it happened).

I've talked to several people about the situation.

The president has stated that the country doesn't require assistance.

With a similar logic, the Present Perfect is used with unfinished time periods like since, so far, up to now, recently:

I've made many new friends recently.

He hasn't been the same since the divorce.

That lady has lived here all her life.

I've lived here for 3 years.

Note that if we're evoking a finished time period, the Past Simple must be used:

I've seen her a few times recently. BUT I saw her a few times yesterday.

With expressions like today and this month, it depends on the context:

I've been on the computer today. (I continue to be on the computer)

I was on the computer today. (I'm not on the computer anymore)

We also use the Present Perfect for experiences:

Have you ever seen a black swan?

Apparently, she's watched every single film in that list.

I've made that mistake before.

...with superlatives:

That's the dumbest thing I've ever heard.

...for talking about change:

You've made a lot of progress.

...for giving news:

Argentina has just won the World Cup.

...to say something is now completed:

I've done everything you asked.

Your download has finished.

The Present Perfect is more common in British English than American English, which has a tendency to use the Past Simple instead. It's still possible to use the Present Perfect in the same way in American English, although the Past Simple is usually preferred whenever an action is considered finished.

Present Perfect Continuous

We use the Present Perfect Continuous for longer or repetitive actions that started in the past and continue in the present:

My phone has been ringing all morning.

I've been trying to reach you.

My uncle has been saying the same thing for years.

...for activities that are temporary or unfinished:

I've been working from home lately.

Trudy has been acting quite strange.

I've been reading a book about alien encounters.

...with how long..? for activities that continue in the present.

How long have you been working here ?

There isn't always a clear distinction between the Present Perfect Simple (usually just called the Present Perfect) and the Present Perfect Continuous, but using the PPC can help clarify that the action happened continuously. Picking some of the previous examples:

I've tried to reach you. (it's not clear if I've tried to reach you only once, or more times)

I've been trying to reach you. (I've made several attempts to reach you)

Trudy has acted quite strange. (it's not clear if this was an isolated event, or if she has "acted strange" more than once)

Trudy has been acting quite strange. (I've noticed her behavior multiple times)

In other cases, the distinction is more clear:

I've read a book about alien encounters. (I've finished reading the book)

I've been reading a book about alien encounters. (I'm still reading it, I haven't finished)

As with other continuous tenses, we don't use the Present Perfect Continuous with non-action, or stative verbs:

I've known her since we were kids. NOT I've been knowing her since we were kids.

Questions in the Present Perfect Continuous are made in the following way:

(question word) auxiliary subject been verb+ing
How long have you been working here?
What have you been doing all this time?
Have you been crying?

Short answers are the same as in the Present Perfect Simple.

Have you been crying?

Yes, I have. / No, I haven't.