Q:

How did Cooper and Brand survive Gargantua's gravity?

Cooper's spaceship travels around (and very close to) the event horizon of Gargantua. 
Romilly explains to Cooper...   

Romilly: Gargantua's an older, spinning black hole. It has what we call a gentle singularity
Cooper: Gentle? 
Romilly: They're hardly gentle, but the tidal gravity is so quick that... ...something crossing the horizon fast might survive. A probe, say.

Now even if we consider that Cooper's ship was going at a very fast pace, how did he and Brand survive Gargantua's gravity?
Note: I'm assuming the fact that Gargantua is a black hole and should have immense gravity. So even ahead of the event horizon it should be huge.

A:

If you're in free fall, the gravitational force has no effect on you at all, no matter how strong it may be. The only thing that causes problems is the tidal force, which is the difference in the gravitational force between your top and your bottom. 
The bigger the black hole, the weaker the tidal force at the event horizon. This question  calculates you need about ten thousand solar masses to make crossing the event horizon survivable.
For a black hole massive enough, the tidal forces at the event horizon could be even weaker than Earth's tidal forces from the moon. Since the mass of Gargantua is said to be at least 100 million solar masses, the tidal forces encountered could very well be imperceptible.

