In general, the Present Perfect Simple‏‎ (PPS) is used to talk about an event which happened in the past but which has a very strong connection to the present:

I have just finished laying the table so we can eat soon.

The Present Perfect Continuous‏‎ (PPC) on the other hand is used to talk about an event which started in the past and it still going on now:

I have been cooking since early this morning but I will finish soon.

Having said that, however, the two tenses overlap a lot and which one we use is often an arbitrary decision and both are equally acceptable:

I have lived here since 1978.

I have been living here since 1978.

Subtle Differences

Some people believe that by using the PPC we are putting more emphasis on the action:

I have been living here since 1978; yes, in this very house; living here every single day of my life!

Contrast this with the PPS in which the time element is more important:

I have lived here since 1978; imagine that, 1978. over 30 years ago!

And sometimes the PPS is more focused on the result of the action:

I have lived here since 1978 and I think that it’s time I moved; this place is horrible!

Because the PPS is more about the result, we tend to use it when the action is completed:

I have lived here since 1978 but now I’ve bought a new house and I’m moving there today!

Again, contrast this with the PPC where the action could well be continuing now:

I have been living here since 1978 and I intend to live here for the rest of my life!

Useful Links

Present Perfect Simple‏‎ in English Grammar – about the PPS

Present Perfect Continuous‏‎ in English Grammar – about the PPC

Simple or Continuous Verb Form?‏‎ – in general, which to use