How hard is it to add to your family of pets?

We have a few pets already and are wondering about adding. The issue is that most of our pets are getting older and wonder if bringing a new pet would make them upset.
We are not for sure going to do this but this is why I am asking ahead of time.
Do pets seem to adjust ok? Can you bring home a pet and see how it goes before you commit?

What have your results been with older dogs and cats and bringing in a new pet?