The Quick Thermal Paste Guide
Between your processor and its heatsink, there is a thermal interface material (TIM). This material helps improve heat transfer from the processor to the heatsink (in hopes that heat will then be transfered to the air). Other heatsinks (such as the one on your motherboard's chipset, or your video card) will also normally have some sort of TIM. For simplicity, we will refer primarily to prcoessors here, although the general concepts apply to any such interface.
"Thermal interface material" is a generic term that encompasses a variety of materials that serve this purpose, including thermal pads, thermal pastes (also called "thermal greases", "thermal compounds", and other terms), and thermal adhesives.
A TIM is a material that conducts heat well. That is its job in a nutshell.
The surface of your heatsink and the surface of your processor are not perfectly flat. As a result, they will not mate up perfectly. This results in a small air gap between them. The trapped air acts as a thermal insulator, impeding the transfer of heat to the heatsink. This, as you might imagine, is bad.
A TIM fills in those gaps. TIMs are always either malleable (like a thermal pad, which when new is soft enough to deform with your fingers) or a liquid. And the TIM is also a better conductor of heat than air. The net result is that heat is moved away from the processor more effectively, and the processor stays cooler.
The ideal TIM is an extremely thin layer of material that is just enough to fill the gaps that would otherwise occur between the two surfaces. Less is more, so to speak.
There are several types of thermal interface materials, each with different strengths and weaknesses.
Thermal pastes are thermally conductive liquids, and are usually fairly viscous. White used to be the standard color for thermal pastes, but since the introduction of Arctic Silver (which you can buy and help this site; all subsequent Amazon links on this page are affiliate links) silver has become popular. Aftermarket heatsinks have long relied on thermal pastes, and some users used to replace the thermal pads on stock processor heatsinks with aftermarket thermal paste.
Processor heatsinks now all use some sort of thermal paste — often very viscous "bubble gum" thermal paste, which might be grey or, more rarely now, pink — instead of a thermal pad. This is often preapplied at the factory in a small patch or series of lines.
If you take a thermal paste, and add an adhesive to it, you have thermal adhesive. The chemistry involved is not quite as direct as that, but the basic principle is not complicated. Thermal adhesives are very similar to thermal pastes, but are designed to adhere the two surfaces together. Thermal adhesives are popular for heatsinks on smaller, lower-power components such as motherboard southbridges. It is usually a very bad idea to use thermal adhesives on a CPU heatsink, as it will then be impossible to remove the CPU from the motherboard.
Many thermal adhesives are thermal epoxies, and are sold as two different liquids in separate tubes. The liquids are mixed in the application process, and when they react they can serve as an adhesive.
Thermal pads are relatively thick (about 1/8 inch), soft black pads normally around 1 inch square. They are favored by manufacturers because they are very simple and reliable to install. Processor manufacturers have moved away from thermal pads for user-installed heatsinks as processors have started producing significantly more heat, because thermal pads are relatively poor thermal conductors. Motherboard chipsets and video cards still use thermal pads some of the time.
Many thermal pads are "phase change" materials that melt when heated. This helps them function as a better thermal interface, but also means that removing a used thermal pad takes a little doing.
Most heatsinks for computer components now come with some sort of thermal interface material already applied. This is meant to make life easier for the end user (you). For motherboard chipsets, video cards, and so on, the heatsink is normally already completely attached (unless you buy a third-party replacement). But processors (and their heatsinks) are sold separately from motherboards, so the heatsink is left for the user to install.
These heatsinks normally have some sort of TIM applied at the factory; these days it is usually an especially viscous thermal paste. Although a small square was once normal, Intel has taken to arranging their thermal paste into a small bit of abstract art.
If you are a typical user, this preapplied stuff is probably perfectly fine for your purposes. Users that want to overclock or are otherwise looking for the best possible performance from their heatsink will often replace the supplied TIM with third-party thermal paste. If that sounds like you, keep reading (but first, if you are using an aftermarket heatsink, check to make sure it isn't already using a rather high-end thermal paste).
If you are looking to buy your own thermal interface material, you probably want thermal paste. It offers better performance than a thermal pad, and is easily removable (unlike thermal adhesive).
For the overwhelming majority of users, whatever happens to be cheaply available is the best choice. The performance difference of most thermal pastes is not enough to matter. Cheaper pastes may dry up faster and need to be replaced sooner, but that's about it.
Overclockers and other "tweaker" types, as usual, may want something more exotic. Arctic Silver 5 is still the canonical thermal paste, but Arctic Cooling's MX-2, Tuniq's TX-2, and Arctic Silver's own Arctic Ceramique (which lacks Arctic Silver 5's slight electrical conductivity) have made inroads. The differences between them, in practice, are not huge.
Most users that need a thermal adhesive, again, will be adequately served by nearly anything they can get their hands on. For those that really want better performance, Arctic Silver sells two thermal epoxies.
Thermal pads are generally difficult to find in small quantities. Amazon has some, although we cannot vouch for their quality.
Now we have entered the bizarre world of superstitution, speculation, and anecdotal evidence. Don't worry, this can all be done without any waving of dead chickens.
If you are replacing an existing TIM, the first thing you need to do is clean off the old stuff. High-concentration isopropyl (rubbing) alcohol will do the job just fine and is available at many drug stores. A variety of other chemicals (naphtha lighter fluid, acetone, plain water) will also work with varying levels of effort. Note that acetone is bad for both plastics and humans. Others (such as nail polish remover, which contains acetone) are likely to leave unpleasant residues behind. There are also products made specifically for this purpose, if you have money to burn.
Apply a small bead about the size of an uncooked grain of rice to the center of the processor. Press the heatsink down. The pressure will gradually spread the thermal paste. If you reall yfeel like you need to "do" something, feel free to use a razor blade or credit card to spread the paste over the processor a bit. Arctic Silver's illustrated instructions, while somewhat overwrought, are illustrated and pretty easy to follow.
You may need to mix the components first, but after that the application should be about the same as thermal paste. Do consult whatever instructions came with the stuff. Be sure you get things lined up correctly the first time, as you may not get a second try.
Peel off one piece of protective film, lay the exposed side of the pad down squarely onto the processor (it should stick a bit). Remove the other piece of protective film, and install your heatsink.