The CPU (Central Processing Unit) is arguably the most important component in a computer. In Layman's terms, it can be likened to a brain, all data is processed in it and reacts accordingly. It connects to the motherboard through a socket and through this connection, has access to all the components of the computer. Modern processors are relatively small, measuring no more than 2 inches. Featuring billions of transistors, the processor is one of the most advanced pieces of technology, now commonly used to look at pictures of cats.
CPUs featuring more than 1 core per die are said to be multi-core. Almost all CPU's that are made today are multi-core, meaning they feature 2 or more cores per CPU die. Many laptops today feature CPUs with 2 cores. Desktop computers can feature 4 or more cores. Common core configurations include single-core (1 core), dual-core (2 cores), quad-core (4 cores), 6 core and on very high end devices even 8 cores. AMD also sells processors with disabled, malfunctioning cores at a lower price. These include, but are not limited to, single-core and triple-core processors, which are respectively dual-core and quad-core processors with a disabled core. It may sometimes be possible to unlock a disabled core, but remember that these cores are disabled for a reason and like over-clocking, unlocking them will most likely void your warranty.
Single-core processors in desktops are mostly considered legacy devices nowadays, but more cores are not always better. Many games fail to use more than two threads (or two cores) and while a processor may be fast with all its cores enabled, a CPU with a lower number of cores but with higher performance per core will probably do better in most games. Like the clock speed of a CPU, the amount of cores should not be directly used as a guide to choosing the fastest one.
CPU speeds can range anywhere from 1 GHz to 4 GHz at factory settings. Speeds for a CPU are measured in terms of MHz (megahertz) and GHz (gigahertz), and measure the speed of the clock signal going through the CPU. CPU clock speed or core count should not be used to judge weather or not different CPU types (e.g. An Intel Sandybridge 2700, and an AMD FX Processor) are better, however they are comparable inside the same series of processor (see see Megahertz Myth).
Turbo is the name for the technology used by Intel and AMD to run a CPU at a higher frequency when it is stressed. For example, an Intel Core i7 2600k runs at 3.4 GHz stock, but turbo increases it to 3.8 GHz. This is especially useful for gamers, as Turbo technologies often kick in when not all cores are used, as is often the case while gaming. If you experience stuttering in games, temporarily disabling this feature is a common fix.
Overclocking forces a processor to run outside factory spec at higher clock rates.
Now, there are hundreds of motherboard and processor combinations, so giving precise instructions to overclock would be nigh impossible. However, many people have created wonderful, comprehensive guides for specific processor models. Use a system information tool (such as Speccy) to find out the name of your processor (generally speaking, numbers in the name doesn't matter too much as the overclocking method will be the same) and then Google "*name of processor here* overclocking guide." With newer processors like the i5 3570k and the FX-8350, overclocking can be as simple as booting into the [[Wikipedia:BIOS BIOS] and changing a single value, even downloading a software tool and overclocking without reboot. For older or lower end processors, the process can be quite a bit more difficult but never really taxing. Do take note, the quality and features of your motherboard will effect how high you will be able to go while maintaining a stable environment. A reputable brand and a decently priced board will suffice for most. However, bottom of the barrel boards will hold you back significantly, even to the point of not being to overclock at all.
Some CPUs can feature combined graphics capabilities. These graphics capabilities may be adequate for web surfing, but are often not adequate for high end gaming. Intel's first CPU line that featured these capabilities was their Nehalem architecture. AMD also provides CPUs with on-board graphics under the Fusion name. AMD calls these chips APUs (accelerated processing unit) and they are much faster than their Intel counterparts at this time. While Fusion APUs will also not provide a great high end gaming experience, most games will run quite well on these chips, even though the graphical fidelity might need to be reduced to achieve reasonable frame rates.
Intel are a favorite with PC gamers, offering better single threaded performance. In terms of gaming, Intel has a solid lead on the competition, not to say AMD processors can't play games well. A good choice for an Intel processor is the i5 3570k, as it is the best quad core they offer without unnecessary features that don't improve game performance.
Intel's initial offerings in the consumer GPU space were under the Intel Graphics Media Accelerator (GMA) brand, and served only to provide basic video functionality to PCs. Very near the end-of-life for the GMA brand, Intel's chipset integrated chips began to compete with older, very basic GPUs from Nvidia and AMD; they are able to play old games at reduced settings. Recently Intel began moving away from chipset integrated graphics, and with the Core i3/5/7 line of chips began offering GPUs combined with the CPU. The current best offering is their HD4000 graphics core, found in some Ivy Bridge chips; it is capable of competing with basic cards in the current generation.
AMD processors are often cheaper than their Intel counterparts, but recent Bulldozer CPUs have been less comparable in terms of their performance. AMD processors offer a trade off of less single thread performance for more cores. Using a similarly priced AMD processor over an Intel processor will, most of the time, incur a small performance hit in games while holding quite an edge over the Intel processors in well-threaded productivity software, such as video editing suites. These Fusion APUs are available for both embedded appliances as well as desktops, the latter using the Llano architecture, are mounted on socket FM1 and are sold as A4, A6, A8 (2, 3, 4 cores respectively) processors. There is currently also an E2 line-up available with 2 cores. The fastest GPU offered by the Fusion series is the HD 6550D, which trades blows with the NVIDIA GeForce GT 240 for gaming performance.
Some older AMD processors (notably the Phenom II and Athlon II lines) are still in use and offer some modern necessities like DDR3 support. Combined with the ready availability of AM3 socket motherboards and a low price, AM3 socket CPU's can make a good CPU for a budget build.
To put this shortly, there is absolutely no way someone could tell you what processor to get. As a rule of thumb, Intel is 10-15% better in single to quad threaded tasks and AMD sees a 10-15% lead on 6 and 8 threaded tasks. This is in no way a be all and end all judgement. There will always be exceptions to this generalization. A good way of judging which brand to go with is to evaluate what software you use. Do you constantly render videos in an application with a format that can take full advantage of 8 cores? Do you solely play Starcraft? The best way to find out is to Google benchmarks. Make an informed decision. And remember, the reason someone bought a specific processor is as individual as the person them self. Do not judge, discriminate or harass people because they bought a processor with a different sticker on the box.
When a CPU is malfunctioning, the problems can range from something as simple as higher temperatures to the inability to boot. The first step is to thoroughly test all other components to make sure that the CPU is the problem. If you are still certain, monitor the CPU temperatures with CoreTemp. If temperatures regularly go over 70 °C, then you may have a heat problem. Make sure that the heat-sink is fully fastened, and if it is, make sure that you applied a proper amount of thermal paste (Note: checking the thermal paste will require you to clean off and then reapply more thermal paste, so only check this as a last resort.)
Another problem that may arise with the CPU is improper seating. If you are experiencing random freezes and blue screens, you may have bent pins on the CPU. To check this, you must separate the CPU from the CPU socket (check your CPUs documentation on how to do this) and visually look for bent pins.
Choosing a CPU is almost an entirely subjective and individual decision. No one can ever tell you what you are going to do with your hardware, so pick the appropriate brand and model with the features you need. While synthetic benchmarks are a good method of ranking processors, they should never truly decide your purchase, especially as some benchmarks (like Cinebench) are actually biased to Intel. It's best to use real world benchmarks. The best advice is to research potential purchases for information regarding what you will be doing with it.
A common misconception, especially to novice buyers, is that the higher the clock speed on a CPU is (the clock speed is easy to find and looks something like 2666 MHz or 3.2 GHz), the faster the CPU is going to be. This used to be the case many years ago and is still the case when comparing processors from the same architecture. For example, an Intel Core i3 2120 is clocked at 3.3 GHz and is faster than an Intel Core i3 2100 which is only clocked at 3.1 GHz, a 200 MHz decrease. This is valid because the clock speed is the only difference between these two processors. On the contrary, however, an Intel Core i3 2120 at 3.3 GHz will be vastly slower than an Intel Core i5 2400, which is actually clocked 200 MHz lower at 3.1 GHz, because of various other factors like the amount of cache memory on the chip, the number of cycles needed to complete a certain instruction, the number of cores and several other factors.
A good way of telling if a CPU is faster than another is to look at benchmarks. Benchmarks are tests where processors are put to work and are compared in their real world performance afterwards. A simple Google search can give plenty of results for almost any CPU. Remember to do your research before spending money on a processor.
CPU article on Wikipedia