The modifications listed in the above writeup are commonly known as "bolt-on" (i.e. they can be easily installed by attaching (bolting) it to some part of the car). However, hard-core performance enthusiasts sometimes try these non bolt-on mods. These are the mods that require super-high-octane fuel, and destroy your engine if you don't know what you are doing.
Increasing Compression Ratio
(This modification is not effective on engines with superchargers or turbochargers) The compression ratio measures how much the fuel-air charge is compressed before the piston reaches top dead center (TDC). It is expressed as a ratio in the form X:1. Car engines usually have compression ratios of about 8:1 to 10:1. The compression ratio can be increased by milling some metal from the engine head or switching to domed pistons. Increasing compression ratio increases fuel mileage as well as power, so it is especially desirable. However, increasing the compression ratio beyond 17:1 will actually reduce power and efficiency. Also, high compression ratios need a LOT of octane to prevent knock. Increasing the compression ratio from 9:1 to 17:1 will yield a power and efficiency boost of about 25-30%.
Optimizing Spark Timing
(DO NOT TRY THIS WITH A NITROUS OXIDE ENGINE!) When the fuel-air charge is ignited (in terms of piston position) is critical in determining whether an engine makes optimum power or not. If the charge is ignited too soon, some of the energy produced will fight the upward motion of the piston, stealing power. If the charge is ignited too late, the charge will become less compressed, which also steals power. However, the spark timing is not always optimum, because such a setting would increase the octane requirements. Retarding the ignition timing (making it ignite too early), creates a slight power loss, but the substantial decrease in octane requirements make it worthwhile to the manufacturer. However, if you have super-high-octane fuel, the octane concern becomes groundless. It can be difficult to determine the exact optimum spark timing, but once you do, the timing can be adjusted in the distributor using special tools. If the timing was way off, optimizing it can gain you about 10% horsepower and efficiency (like compression ratio, optimizing spark timing increases efficiency as well as power.)
(Not recommended for engines with turbochargers) This modification is unlike the other two. Instead of increasing the efficiency of the engine, which leads to more power, this mod shifts the torque curve, which can lead to more horsepower, albeit in a different RPM range. Since power is proportional to torque times speed, shifting the torque peak to a higher RPM (speed) range will produce more horsepower. However, the horsepower will only become usable at a high RPM level.