Dress entirely in black. Black jeans and a black turtle neck usually work. Whatever you do, make sure that your black clothes are tight, not baggy. Wear a black hat on your head. A beret, or a newsboy hat turned backwards will help you achieve the desired look. It is also recommended to wear glasses of some variety. Black sunglasses (which a Hep Cat can wear indoors or outdoors) are a good choice, but horn-rimmed reading glasses are a good substitute if you want to see.
Shave your beard into a neat, round goatee. Move the razor carefully around the desired spot, and make sure not to miss any unwanted hairs. You should end up with a sleek, modern tuft of hair on your chin, with very clean lines.
Put some jazz or swing records on your turntable, and play them through. Duke Ellington records are recommended. Snap your fingers along to the records. You can snap your fingers by pressing your thumb to your middle finger, and pushing your middle finger into your thumb until it hits the center of your hand. Once you can get into a groove snapping your fingers and listening to jazz records, you will have all but perfected your Hep Cat look. Once you feel comfortable, go to your local jazz club and snap along to live performances.