I have spent a lot of my life taking photos in low light situations - middle school dances, high school parking lots after marching band, nights out with friends, and Disney. These came in handy this weekend at the bachelorette party, I tell you! Here are the guidelines I use for low light.
this is a terrible photo. 5 years ago, i thought i should photography a strawberry using flash, apparently.
Do not use your on camera flash (I beg you, for most things)
I always enjoy watching the confusion when someone takes flash photography on a Disney ride or ran up to an aquarium tank to get a shot of a fish. Most of the times, it's a big white blur. On camera flashes are usually too harsh (and really cheap, tiny flashes) and do not help, but hurt your images. I always have my cameras (point and shoot and even my cell phone) set to a no flash mode. Instead, take advantage of the lighting around you, even if it's limited.
Change your ISO
You can see more about ISO in this post, but quickly, low number ISO for lots of light, high number ISO for low light. When you walk into a building, chances are you should go up a bit from when you were outside. At night, you're looking at cranking it up pretty high. I try not to go past 1000 or 2000. My camera and lots of new ones go up to 6400 but you will see significant grain at this level. For a shot aimed at capturing a memory where you are less concerned with it's 'artistic value' 6400 will do as it is least likely to blur even in a dark restaurant.
Tripod or Ground Yourself
Tripods are ideal for low light settings, but if it's weird to set up a tripod, try making yourself a tripod. Prop your elbows onto a table and lean in - hold the camera firmly between your hands and shoot.
Be sure to shoot on burst mode! Your press of the camera shutter button will cause movement, and your camera picks up on those movements, shooting on high speed burst ensures a shot in the middle doesn't have the movement from your press and release of the shutter button.
Find the Light
Find lit objects, like light fixtures, and stand closest to those to shoot.
Put your aperture to the lowest setting. If you have multiple lenses, switch to the lens that has the lowest f-stop (f/1.8, f/2.8).
Focus on Non-Moving Objects
Try focusing on something that is on the same plane as your subject (especially if your subject is moving a lot) then moving your switch to manual focus. Don't move, and take a few shots! This is particularly great for zoos and aquariums.
Okay, so You Need Flash?
-Edit after the fact.
-Don't shoot into mirrors. Oops.
-Try bouncing the flash off of a card or piece of foil. There are a lot of techniques to basically create a really cheap reflector on the internet. Check these out. I've used the party bouncer card before, I can admit.