By changing your exhaust, you can make your car produce more sound, which will be a good first step toward making your car sound like a Ferrari. Second, you should try to increase engine revs as much as you can, as this will more closely resemble the sound produced by a Ferrari engine. Finally, an aftermarket air intake will give you a better "suction" noise, and even though your car won't sound exactly like a Ferrari in the end, it will certainly be closer than when you started.
A Ferrari produces a loud sound, whereas most road cars are designed to produce less notable sound levels. Especially at high engine speeds, exhaust bypass valves open on many Ferrari models (the F430, for example) to produce more power and a richer and louder exhaust note. So, the first thing you can do is to purchase an aftermarket exhaust designed to produce a richer and louder exhaust note. Select a high quality unit and ask the manufacturer for sound clips from an engine similar to yours before you buy.
Increase peak revs. Ferrari engines spin extremely fast and therefore produce a high note as they approach peak revs (think of the constantly higher note made by the washing machine as it spins faster and faster during the rinse cycle). The Ferrari F430, for example, produces peak power at 8,500 revolutions per minute (rpm) whereas most engines will not even allow you to reach such high rpm. The engine management computer on most road cars will cut off ignition or fuel supply when you exceed the top of the rev range to save the engine. In most cars, you can raise the limit at which the computer intervenes by uploading a new software onto the vehicle's electronic control unit. Several tuners offer such software, which you can either download yourself or have a professional install on your vehicle. This may not be healthy for your engine, however. The engine's manufacturer determined the rev limit to maximise engine longevity.
Get an aftermarket air intake. Part of the Ferrari's unusual and widely recognised sound comes from the intakes sucking air at high speed. Since most Ferrari engines are behind the driver, the intakes are usually positioned fairly close to the driver, on the side of the vehicle. While you cannot place the air filter of your front-engined vehicle on the side, you can purchase an aftermarket air intake system, designed to feed more air to the engine. Such systems, also known as "cold air intakes" are relatively inexpensive and will slightly increase peak horsepower of your vehicle. As they let in more air, they will also produce more of a suction sound.
A Ferrari engine has many other design features which are impossible to replicate on a conventional engine with aftermarket parts. These changes, however, will make your engine sound better and more like a Ferrari than it did.
Proceed with caution when raising the rev limit of your engine. Carrying out this operation without proper research can lead to engine failure. After raising the rev limit of your vehicle, ensure that the engine is properly warmed up before you rev it near its new limit.