Here's my understanding as a backyard astronomer...
First, gravity is more accurately defined in Einstein's STR as energy that bends space/time (because energy and mass are linked by E=mc^2)(1). So let go of Newtonian mass attracting mass. A black hole then is a huge energy source that is warping space/time initially incredibly deeply, but then tapering off according to the inverse-square law.
The event horizon (EH) is defined as the boundary where anything with mass, which includes light, has to travel more than the speed of light (c) to attain escape velocity. As c is the absolute upper limit on speed, nothing can escape and the 'hole' is 'black'. (2) Trying to calculate what is going on within the EH is fruitless, as current equations tend to return "Divide By 0"! ;)
So, with the mass of the singularity warping space/time causing what we call 'gravity', gravity itself doesn't have to escape anything - it just is.
Thus a black hole can be observed exerting a gravitational influence on objects around it, such as the observations of stars and stellar clouds in orbits around Sagittarius A* (3)
As per any gravitational system, an object may be attracted towards a black hole and then ejected, it may be in a stable orbit, or it may be spiralling inwards to eventually be torn apart by tidal forces and join the accretion disc around the EH. Here it may fall in to add to the mass of the singularity or may be radiated by the energy of the accretion disc and jets (4).
If a system consists of binary black holes, they might orbit one another until eventually spiralling into each other and merging in a cataclysmic event that the LIGO team recently detected (5)
Hope that helps a bit!