I worked in a vet clinic, and we only rarely cleaned cat's ears so you should make sure that the cat needs it first because it will not enjoy the cleaning. First, you need to buy cleaner that is formulated for cats and dogs. Next, have someone else hold the cat while you put a squirt down the ear. Then you should massage the ear from the base up. After that you can wipe out of the ear with a bit of cotton ball. When those are coming out clean, use Q-tips to clean the folds inside the ear.
Clean your cat's ears quite often, as dirty ears could lead to infections and parasites. To do so, you'll need some cotton balls, q-tips, some tweezers, and of course, solution to wash your cat's ears. Only clean their ears when the cat is calm, rather than distressed or annoyed. For more instructions, go to the link below. LINK: http://www.vetmed.wsu.edu/cliented/cat_ears.aspx