Q: Do the memories stored in a Pensieve reflect reality or the views of the person they belong to?
A: It's reality. It's important that I have got that across, because Slughorn gave Dumbledore this pathetic cut-and-paste memory. He didn't want to give the real thing, and he very obviously patched it up and cobbled it together. So, what you remember is accurate in the Pensieve.
Q: So there are things in there that you haven't noticed personally, but you can go and see yourself?
A: Yes, and that's the magic of the Pensieve, that's what brings it alive.
Dumbledore keeps his Pensieve in a black cabinet in his office. When he has too many thoughts and memories crowded into his head, he siphons the excess thoughts into the basin using his wand. He says that "(i)t becomes easier to spot patterns and links" in the memories when they're collected in the Pensieve (GF30).