A person is usually a regular officer before becoming a K9 handler. There are many kinds of K9s: some sniff for narcotics. Some sniff for explosives. Others look for people, including burglars hiding in a warehouse.
Just like with officers, there are "routine days" and days that get crazy wild. You could have days where nothing happens.
K9 officers spend a lot of time doing training with their dogs. Once school is over, you have to keep the dog current so he remembers what he learned. It is also important to keep real good records of his training. If an officer made a drug arrest because your dog alerted to the presence of narcotics, you might go to court to testify about your dog's training records and also how exactly the dog "told" you there was something wrong.
K9 officers also do community relations. They go to schools and public gatherings and do performances, and answer questions about their dogs. Everyone loves dogs, so this is real good public relations for the police.
You will also spend time taking care of your dog. Walking him, grooming him, taking him to the vet, cleaning out the patrol car. These dogs tend to be hairy. It's important to keep him well-groomed, because people don't like it when you leave dog hair behind! Imagine how much dog hair a bomb dog could leave on all the seats of an airplane!
K9 officers are on-call. If there are a lot of K9 officers in the department, this will usually be rotated. But if it is a smaller agency, you might be on call all the time. Also they sometimes get sent to other cities, sometimes for several days. Suppose the event planners for the SuperBowl want to "sweep" the stadium before opening the doors. That one city may not have enough dogs, so they request help from other agencies.
Also, keep in mind a dog cannot work for 8 hours, so after a while he will need to rest before being put back to work. While your dog is resting, you can work on your paperwork, or you might be given other assignments, such as handling regular calls, directing traffic, etc.
I was never a K9 officer, but I am close friends with an officer who is a trainer/evaluator for TSA. He previously worked with me at the Airport PD.
Hope this helps!