It's not all about increasing horsepower.
Going faster is not always about straight line speed. How a car handles and brakes are pretty important too. This is especially true if you enjoy driving on twisty mountain passes or race tracks. Yet there are hundreds of tuners out there who merely focus on the max horsepower and torque numbers without giving much thought to the rest of the package. Going this route can be expensive and may drastically shorten the lifespan of the non-upgraded components in your car. As you're about to discover, improving overall performance can be done on a budget.
Regular maintenance including a new set of spark plugs, good quality oil and new filters will not only ensure that your engine is performing as intended but it will last a lot longer too. Sludgy oil, clogged air filters and spark plugs that have been left in too long will all have a detrimental effect on performance. Brake fluid can also absorb moisture over time which may make it boil over in enthusiastic driving. Watch out for clogged catalytic converters as they will reduce power levels and can damage other engine components too.
Regardless of what type of internal combustion engine you have it needs air and fuel to make it go. The more it gets the more power it makes. Higher flow injectors and fuel pumps will ensure that the cylinders get enough fuel to keep the air-fuel mixture at optimum levels. Turbos and superchargers essentially force air into an engine, nitrous oxide injects a concentrated shot of oxygen into the combustion chambers. None are particularly cheap so for our purposes we will need to stick to a cold air intake which can help aid the flow of air into the engine.
Assuming everything else is equal, a car that weighs 4,000 pounds will need 400 hp to keep up with a car that weighs 2,000 pounds with only 200 hp. It will also need bigger brakes, tires and upgraded suspension components to handle well. It stands to reason that carting around a massive sound system and various bits of junk in the trunk is going to slow you down. If you are going to a track day then remove the rear seats, spare wheel and trunk carpeting. The 100-pound weight saving will make your car accelerate a tiny bit quicker and will put less strain on the brakes and tires.
Good quality tires are essential to achieve the best cornering, traction and braking performance. Skimp on these and you will either be fighting for grip at the lights, sliding out around corners or having unfortunate encounters with stationary objects. Tires, along with powerful brakes and a decent suspension system will also improve your lap times way more than just cranking up the horsepower.
Brakes can often be the afterthought when modifying a car for better performance. They are in fact one of the first things that should be upgraded as any improvements in acceleration will inevitably put a strain on the braking system. Start off with a set of decent road/race pads and move on to better rotors when your budget allows. Remember to upgrade your brake fluid and brake hoses too. Fitting pads and rotors that are intended for track use to your daily driver is not always a good idea though. They generally need some heat in them before they perform properly and they can also squeal terribly when cold.
On older cars, new suspension bushes and shock absorbers can transform the handling feel. On newer ones lowering kits can aid in cornering ability but don't go too low as you can damage the undercarriage over bumps. Any upgrades that improve handling generally stiffen up the suspension which makes a car lean less in corners, while the downside is almost always a much firmer ride.
Remapping has become big business with the proliferation of turbocharged engines. It is relatively easy to get up to 20% more power and torque simply by changing the software coding on a modern ECU unit. As tempting as it is to crank up the boost until your Civic spits flames and shreds its front tires, it is best to stick to reputable specialists who offer a warranty and do not try to wow you with massive power gain claims. The increased power will put additional strain on the rest of the cars running gear so consider carrying the remap out in conjunction with other upgrades too.
Every car has a drive belt that powers the auxiliary systems such as the power steering, alternator and water pump. This robs the engine of power. An underdrive pulley essentially runs these systems at a slightly lower speed which frees up some extra horses. Air-conditioners are one of the worst horsepower parasites and you can save power and reduce your cars weight by removing the system altogether.
Depending on what state you live in (California is especially strict), you can upgrade your exhaust system with a less restrictive aftermarket system. This can liberate some extra power and generally increase the noise levels. If your car has a six-cylinder or V8 motor then that is a good thing. Four-cylinder engines on the other hand do not always sound great, and some systems can be too noisy at highway speeds. Do your research first on this one.
Regardless of how quick your car is on paper, unless you know what you're doing you won't be matching those figures on the road. Even if all you plan to do is race people in a straight-line, an advanced driving course will help you understand how to extract the most from your car and keep you safe. If you don't know what you are doing you will have wasted all that money on the go faster bits anyway.