Honestly, it varies a little depending on the cat and the new puppy! If a cat has grown up with other dogs around they may not mind and may actually enjoy the company. If the cats never seen a puppy before they may be hesitant or curious. Sometimes a puppy will want to play and could try "pulling" the cats tail or lick them to get their attention. Depending on the cat they may like that or they may not. Usually if the cats irritated, they'll just jump somewhere high that a puppy can't get to like a table, ledge, window sill, etc. We've never had someone return a puppy because their cat or new pup wasn't getting along. Typically the cat will get over their jealousy/ grudge against the new puppy and like being around or observing them.
Below is a video a family had sent to us of their Malti- poo puppy named Remi who was playing with their cat. It's just too cute!
Above is a picture of my own pets. I have 2 cats named Mittsie and Pharoh and 3 dogs named Molly, Mabel, and Romeo. My cats are about 8.5 years old and my dogs vary in age from 1 to 5 years of age. Before I got my dogs, my cats had never been exposed to a puppy before. From personal experience I'd say they get along just fine. They didn't mind being around each other and they all try to sit on my lap (at the same time.) Sometimes my dogs would lick my cats and if they didn't like it they'd just jump onto the top of the couch or another place the puppies couldn't get to them. -Abby, current employee, soon to be Vet Tech