Humans are accustomed to think of the "pet-owning" (forgive me while I expel a hairball of disgust) world as being divided between dog people and cat people. This would be convenient and would give me no need to write this post.
However, to their possible credit, many people describe themselves as "animal lovers." This may mean they are kind-hearted, and if you evaluated them thoroughly when you considered them for adoption, you will already know this.
In other cases, though, you will find a household where a dog person and a cat person combined households. This raises the possibility that, once the glow of love and mating dissipates, they may be in trouble, due to deep emotional incompatibility. This will mean trouble for you, so be on the alert for early warning signs. Your first action must to be to make yourself indispensable to the cat person.
I will cover this area more thoroughly in a post entitled "What Divorce Means to You."
Whatever the reason for a dog being already established in the household you intend to conquer, you must deal with this presence. His seniority need not concern you as much as that of another cat would. It must, however, be taken into consideration.
For this reason, I recommend that you exercise the maximum in self-control. Evaluate the dog. Is her tail wagging? Is she panting in a friendly way? If your impressions are positive, make the most of the opportunity.
If you're a kitten, assume the "I'm just a tiny, adorable, helpless ball of fur" attitude. Move very slowly towards the dog, pacing yourself by the volume and frequency of the remark, "Isn't that the cutest thing?" and by the flashing of cameras and cellphones. If you hear the statement, "We should put this on YouTube," up the attitude and accompany it with heartbreaking whimpers.
If you are a mature cat, don't try to overplay cute. Instead, go for pathos. Remind your new servants that you've had a tough life on the street where you learned to trust no one or that the death of a human forced you into homelessness. Convey with an ever-more-confident step that being in this loving and nuturing atmosphere is already healing your psychic wounds. If you play it right, you, too, may earn Internet exposure.
Regardless of your age, keep the climactic scene well in mind. You will end up crouching or lying between the dog's legs, your head buried against his chest. (I hope for your sake that he will have been recently bathed.) Hold that pose. Humans love scenes of interspecies friendship because they don't understand that we are far more tolerant than they usually are. Or maybe they do understand and need the inspiration of the lion and the lamb and the dog and the cat.
It costs you nothing to make them happy, and you will be greatly rewarded. They will talk about you to their friends, and they will put your picture on their Facebook pages and web sites. You could become famous.
It's worth suffering a small amount of dog hair.