If you are the owner of the site, you can do the following:

1) Open Library settings





2) Select permissions for this document library



 
   (1) If the library inherits permissions from its parent, 
   (2) then Stop inheriting permissions and 
   (3) click "OK"




(1) Add the additional person 
(2) decide if you want to inform this user by mail 
(3) select Contribute or Read access