What part are you worried about? My dogs are pretty laid back, so I didn't have to worry about doing hours of exercise each day.
As far as normal, routine care, babies are pretty portable, so I was able to cart him around while I did various pet things. He was also a much better sleeping newborn (during the day, at least) than he is as a toddler. So I had several naptimes where I could do things. There are also two adults in the house, so one could do baby tasks and the other pet tasks, etc.