Honestly, it varies a little depending on the individual cat! If a cat has grown up with other dogs around then they may not mind and may actually enjoy the new company of a puppy. If the cat has never seen a puppy before, they may be hesitant or even 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 cat's 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 puppy wasn't getting along though. Typically the cat will get over their jealousy/ grudge against the new puppy and like being around or observing them.
Video:
Above is a video that a family had sent to us of their Malti- poo puppy, Remi, playing with their cat. It was too cute to not share! Based off the body postures of both pets, you can tell that they enjoy playing with eachother.
One of our cats, Jojo, snuggling with a black toy poodle puppy of ours
"Above is a picture of my own pets. I have 2 domestic tabby cats named Mittsie and Pharoh and 3 dogs named Molly, Mabel, and Romeo. My cats are about 11 years old and my dogs vary in age from 4 to 6 years of age. Before I got my then puppies, my cats had never been exposed to a puppy before. From personal experience, I'd say that they get along just fine! They don't mind being around each other and they all try to sit on my lap (at the same time... Haha.) Sometimes my dogs will even groom my cats!" -Abby, employee and CVT.