Manually reduce the exposure
If your photos are looking grainy and gray, or the highlights in the frame are a bit blown out, try reducing the exposure to produce a crisper and better-composed shot. To do this, tap the screen to set the focus, then drag your finger down. Keep moving your finger down until the gray graininess is black, and the highlights clearly pop -- in low light you always want to expose for the highlights.
Play around with HDR mode
One of the standout features of the iPhone's native camera app is High Dynamic Range mode, which snaps several photos simultaneously when you hit the shutter, each at different exposures. Your phone then automatically merges them together into one photo, incorporating the best/most well-composed elements of each exposure. In low light, this often results in a final image that looks a lot closer to what your eyes are seeing in real life.