How do black holes affect time?
Black holes do not affect the time in reality, but being in close proximity to one would greatly change your perspective of time.
Time is time, nothing in the universe can change it, however, one's perception of time can change based on proximity an object of great gravity. Mathematics show that if two twins were to be born but one were to spend their life in a space station while one were to life on earth, the one in space would age quicker.
Black holes are very similar, just much more extreme. If you were to somehow be very close to a black hole without dying, you could look out and seemingly nothing would change, but outside it would seem that years and years have passed. This is known as Gravitational Time Dilation.
Black holes have a fundamental effect on time.
Einstein proved that time is a forth dimension of space time. Gravity is not a force, it is a consequence of the slowing of time due to curving the fabric of spacetime
The extreme gravity of a black hole curves spacetime so much that time stops at the event horizon.