Below is an excellent video that shows how to clean a cat's ears:

Ear cleaning is especially important for cats with waxy ears and cats that have ear infections.
Vets always compliment how clean my dogs and cats ears are yet I have never cleaned them. I suppose I won’t always be so lucky as to have such ear wax free pets so I’ll bookmark this one for when that day comes. Thanks!
Ear cleaning is especially important for cats with waxy ears and cats that have ear infections.
“Our cat Fusawo. Just like our children, Fusawo peacefully lets us clean his ears. The inside is very crusty, but he patiently waits until the end!” You don't normally need to swab your cat's ears, but ear mite treatments usually require cleanings.How to Clean Cat Ears Using Coconut Oil - YouTubeFor more information about cleaning your cat’s ears please  PetLife Animal Hospital.
Many cat owners fail to realize the importance of regular ear care for their cat. A cat's ears are very delicate and have a high risk for infections or mite infestations. As a result, it is necessary to inspect your cat's ears on a weekly basis. A regular inspection and cleaning routine helps catch and prevent diseases before they occur. Unfortunately, most cat owners hesitate to take action. They are concerned about hurting or damaging their cat's delicate ears during the cleaning process. Luckily, there are several tips and tricks for good ear care without hurting your cat.
It is important that cat owners are aware of some of the things to look for when cleaning their cats ears that may mean a visit to the Vet. There are a few conditions that can affect the ears that require veterinary attention.
A happy cat makes the cleaning process easier for everyone. Reward your cat after each cleaning. Your cat will be less resistant and will associate the task with a positive experience. Furthermore, make sure cleaning occurs at appropriate times. Don't practice ear care after nail clipping or bath times, as these activities can be negatively associated. Cleaning your cat's ears can be a daunting task, but if you follow these tips and tricks, ear care should soon become easier.Before discussing how to clean ears, it is important to note that the average pet owner should not attempt to clean their cats ears with cotton swabs. Stick to cotton balls. Cats don't like to sit still, they will shake and jerk and using cotton balls prevents the risk that they will accidently rupture the ear and need emergency treatment.Ear Mites called Otodectes cyanotis are a very common and irritating problem. They have a life cycle of 21 days from egg to adult and feed off skin flakes and secretions in the ear. Ears in an infected cat will have dark wax that may resemble dirt. Your cat may scratch and shake its ears and head. They are easily diagnosed by your Vet who will use an otoscope, just like the one in your doctor’s office. The mites are seen as small, off-white dots moving on dark wax. Your cat will receive a medicated ear cleaning and then will be sent home with ear medication in the form of drops.
Cat ears need periodical cleaning as part of the weekly grooming process, to prevent different ear infections and the occurrenceof parasites. The ear cleaning may also be required prior to administering ear drops or medication when your pet is affected by infections or ear mites. Cleaning the cat ears using olive oil is the easiest method, as olive oil is available for anyone.