To get maximum value out of your car, it is important to sell on your own. This is because, when you trade in, the dealership has to cover their costs when reselling, which causes you to get a lower value for the car. Obviously getting the maximum price when selling your car is what everyone wants.
The first step would be to clean it. Either wash yourself or take to car wash, get the exterior cleaned and waxed. This inside should be vacuumed and the small stains in the carpeting and upholstery should be eliminated. Cleaning the dirt and dust off the dashboard is also important. Basically getting it to look as nicely as possible. When cleaning, you can also fix any small defects such as a broken door handle.
Next you would want to make sure the car is mechanically sound. Take it into a trusted mechanic, get a basic oil change done. If needed have air filters and other things replaced. Also, fix any glaring mechanical problems, such as a check engine light. With other mechanical problems, weigh the benefits of fixing versus ignoring, as you may not get a good return on your investment with some mechanical fixes. But do let the new owner know of any issues with the car.
Once your car is clean on the inside and out, and mechanically sound, you would prepare the car sale listing. Their are numerous websites and publications, many of them free. If you are in a big city, you could probably use on of the free ones. With the listing, list all of the car accessories, such as power windows, cd player and so on. Take numerous pictures from the outside and inside from different angles. Once listed with the pictures and descriptions, you should get some responses. You would meet the prospective buyer and person and try and sell the car.
Keep in mind, you can get a general idea of the cars value by looking it up. Look at local market rates and the blue book value. If you can, get a vehicle history report. Especially if the vehicle has a clean history. This will bring value to a prospective buyer, since it will leave them at ease. It is a good idea to meet when banks are open, in case they want to go through with the purchase. This will ensure a smooth transaction.