Start by keeping the new cat in a separate room. This allows both pets to acclimate to each other's smells and sounds before they meet face-to-face.
Allow one pet to roam the house while the other is confined, then switch. This helps them get used to each other's presence in a safe and controlled manner.
Once both pets are comfortable with each other's presence, let them see each other through a barrier.
When both pets are ready, introduce them with the dog on a loose leash. Monitor their body language closely for any signs of stress or discomfort.
As the pets become more comfortable with each other, gradually reduce your supervision. Start by leaving the room briefly, then extend your absences as they adjust.
Ensure the cat has access to elevated spaces where they can retreat if needed. Keep pets separated when you're not home, even if they seem to get along well.
Remember, the introduction process can take weeks or even months.