For an internal-combustion engine to create useful power, it really needs just three things: a fuel and air mixture in the correct proportion, an ignition source (spark plug), and sufficient compression to make the charge pack a punch.
But first, that combination of fuel and air must get into the cylinders — and when the deed is done, the exhaust must be routed back out. At the heart of the induction system is the carburetor or fuel-injection system. (Because fewer simple airplanes have fuel injection, we'll focus on the carb.)
Put simply, the carburetor lives to mix liquid fuel from the tanks with the appropriate amount of air, atomize this mixture, and provide a way of controlling engine speed through throttling of the intake air. Though the chemically correct ratio is 15:1 by weight, aircraft engines will run well on ratios from 16:1 at the lean end to 10:1 on the rich side. (The terms lean and rich refer to the amount of fuel delivered, so a lot of fuel is rich and not much is lean.) It's the carburetor's job to ensure that the right ratio, in the right form, is available to the engine at the appropriate times.
Fuel delivered from the tanks enters the carburetor and is held in the float bowl, so called because a set of airtight floats work against a needle valve to maintain a set level of fuel in the bowl. This is important because the amount of fuel in the bowl in part determines how rich or lean the carburetor runs. (This is a subtle effect and is easily overridden by the mixture control, which we'll discuss shortly.)
In airplanes, you'll find the carburetor at the bottom of the engine, a throwback to the days when the devices were prone to leaking — and dribbling of fuel on a hot engine could be hazardous to one's health. As such, these are known as updraft carburetors, as opposed to the more normal downdraft types found atop automobile engines until a decade ago, when fuel injection pretty much took over. (A relative handful of aircraft have side-draft carburetors, which are functionally similar to the updraft versions.)
Carburetors work by using the flow of intake air through a venturi restriction — increasing the velocity of the air and creating a low pressure zone just downstream — which then draws fuel through a nozzle into the air stream. A fixed orifice, or jet, determines the maximum fuel flow through the carburetor. The nozzle, which resides in the middle of the carburetor throat, also helps atomize the fuel, creating a more uniform mixture.
This simple aviation carburetor also has a mechanism that you won't find on automotive carbs: a user-adjustable mixture control. Why? Because an airplane must operate at a variety of atmospheric conditions, from the oxygen-rich lower elevations to thin-air altitudes. And the basic self-compensating nature of the carburetor — the more air flow through the venturi, the more fuel drawn from the bowl — is insufficient to work adequately across the range of power settings and altitudes. In addition, air-cooled engines require more fuel during takeoff and climb, primarily for cooling and detonation suppression, than they do in cruise or descent. The mixture control operates a needle that moves down in the main jet to decrease fuel flow and lean the mixture.
Once the fuel/air mixture leaves the carburetor, it travels through a series of tubes to the individual cylinders' intake ports. Along the way these tubes twist and turn to accommodate engine-packaging requirements first and the needs of the intake system second. In other words, the typical setup is not optimized for ideal mixture distribution among cylinders. In Lycomings, the intake tubes pass through the oil sump, heating them, as well as the fuel-air mixture and the carburetor itself, which is bolted beneath. This helps ward off carburetor icing — a phenomenon caused by the cooling of the intake air as it passes through the venturi, which causes the dew point to fall and some of the water in the air to condense and freeze on the back side of the throttle valve. Continentals typically do not locate the carburetor next to a heat source, and so some airplanes like the Cessna 150 and fixed-gear 182 are quite prone to carburetor icing.
Exhaust system design is amazingly straightforward in aircraft. Instead of attempting to carefully tune the system for noise reduction and cylinder scavenging, most designers settle for getting the hot gases out of the cylinders with a minimum of fuss. So the typical steel exhaust system will have tubes of the same diameter for each cylinder, but not always of the same length. They will feed into what may appear to be a muffler but is in reality a can with little more than a simple baffle inside.
It's important to understand that exhaust-system integrity is critical. Because the gases can be as hot as 1,500 degrees Fahrenheit at the exhaust port, this blowtorch-like heat must stay away from unprotected surfaces. Also, any leaks in the exhaust system around the heater muff, basically a shroud that uses the hot exhaust pipe to warm the cabin and for carburetor deicing, can lead to poisonous carbon monoxide reaching the cockpit.
Ultimately, what aviation intake and exhaust systems lack in technological "wow" they make up for in simplicity and durability, and with proper maintenance you'll probably never have to think much about these systems in flight.