There would be nothing stopping you building a facebook like application within DNN
 - ultimately a framework like dnn is really only limited by the creativity of the people choosing to use it.

As to HOW - well that is an entirely different story - and it really depends on what you want to do.
Do you want to code and build the functionality yourself to suit your needs - or are you more wanting 
to leverage off what is already around.

If the later then there are a number of social portal type modules available for dnn - have a look on www.snowcovered.com and do a search on the word Social - you should see a list of modules that do the sorts of things you may be looking for.

Have a look at activesocial and vivosocial 

Westa