When introducing a new pet to your current pet you need to try and visualize how you might react or feel if say your parents bought someone home with them, and then said that you now have to share all your toys.
Most animals if not all animals are very territorial, if you are introducing a new dog to your household then it would be a good idea to leave your current dog at home when you go to pick the new one up. Also try and introduce the dogs on neutral grounds, like taking them out to meet each other on walk around your local park, this will hopefully minimize tension.
Try not to force interaction between them, I wouldn't recommend walking in with your new dog and throwing it at your current dog, neither dog will appreciate that, instead let them get on with it themselves, when they are ready to interact they will in their own time. If you really can’t help yourself you could try and encourage them by making the introduction really positive and light hearted, and speak to them in a happy and calm voice.
As we all know dogs like to sniff each other, and there will be no exception here. Let them sniff each other for a couple of minutes then gently pull them away, and then let them sniff again, you could intervene with their interactions with simple obedience here, when you pull them away tell them to sit or lay then reward them with treats, this reminds them that you are still the boss and you are in control and will calm any aggression being sensed by each other.
Body language is the most obvious sign on how a dog is feeling, so watch closely when the dogs interact, if you start to see your dogs getting ready to pounce on each other then they probably going to do so, so get in there quick and separate them. This little and easy method can probably be applied to all domestic animals, not so much with say Hamsters, rabbits, fish, birds, or cats. (Wouldn’t see my cat sitting or lying down on my say so) but the general feeling and what we need to remember is that they all have their territory, and introducing a new pet into another pets territory needs to be considered when introducing a new pet to the family.