Come up with a reason for a secret laboratory. Become a mad scientist or a crazy chemist. Stop showering and make your hair stick up from your head when you're doing your crazy experimentation.
Find a spot for your secret lab. Since the lab is a secret, you'll need a basement, an attic or a special room in your house. If needs be, block off your secret lab from the rest of your house with bricks and mortar and a big steel door.
Keep the spot a secret. Put a lock on the door with a key, a thumb print scanner or even a retinal scanner to keep everyone else out of your lab.
Purchase your equipment. Depending on the experimentation you're planning on doing, you'll need chemicals, beakers, a microscope, sterilizers, incubators and lots of science books. If cost is a factor, purchase second hand equipment.
Come up with an electrical source and a water source. Science experimentation requires lots of electricity and lots of water, if for nothing else than rinsing away spills. Be careful you don't use too much electricity though, or you may draw the attention of your city.