Instructions
Allow the existing pet the same amount of freedom it's always had. Introduce the new pet into the main living space in a pet carrier. Expose the pets to each other in this manner for short periods of time. Do this frequently.
Extend the amount of time the new pet is in the main room with the existing pet gradually, based on how the two interact. Save this step for when both animals appear comfortable with the presence of each other.
Place a leash on the new pet and introduce it into the main living space. Open the carrier door while maintaining control with the leash. Allow the new pet to come out of the carrier when it wants to, rather than force the issue.
Let the animals become familiar with each other with no barriers, using the leash to ensure the safety of the new pet if necessary. Once the animals are very comfortable with one another, you can eliminate the leash and allow the new pet the same access to the home as the existing pet.
How to Introduce New Pets
Introducing a new pet to existing pets takes some time and patience to do correctly. Bring the new pet in with a carrier until both animals are accustomed to each other. Slowly increase their time together, and eventually move to a leash before allowing the new pet free reign.