Some of these tips will be easier to use then others and they can be applied to most pets with the exception of the exotics such as snakes, frogs, spiders and lizards.
The first thing you want to do is make sure their is a spot in your home that is just for your pet. Someplace they can retreat to when they need to be alone. It should be someplace where every family member understands is just for the pet. Whether it is a crate for your new puppy or a bed in a corner for your new kitten, or a plastic igloo for your new hamster or guinea pig they need someplace to escape too.
When you go to pick up your new family member get some of the bedding that is in the cage with your small animal. If you are getting your dog or cat from a reputable breeder see if you can drop off your puppies new bed a couple days early so it gets the scent of home on it. To help close down puppy mills make sure you know where your puppy or kitty comes from. Avoid pet stores because the only way to make sure of where your pet comes from is to get it from the breeder yourself. Now if your like me and get your pet from a shelter then check with the shelter to see if you can drop off the bed before pick-up.
Now to help get the pet use to you faster, before you bring them home take an old worn out shirt (one you don't want any more) and where it to bed (don't wash it). When you bring your pet home add it to their sleep area or cut it into pieces and add it to the small animal bedding. This will help them get use to you faster.
Last but not least and especially important if you have small children. Give your new pet some room to explore their new home with out being mobbed with attention. You should give small animals at least a week before you try handling them. (this of course depends on where you get them since some pet stores do an excellent job of handling their small animals) By giving your new family member some room to explore you will help prevent agressive behavior based on fear.