Well, not just for you, but for anyone else who doesn't know about thermal paste, what it does, and the basics of how cooling works and why it's so important, I'm going to just toss a spiel out.
~~fan~~
||heatsink||
**thermal paste**
{chip}
That is your very basic chip cooling. Thermal paste is made of incredibly small pieces of synthetic conductive metals that make a pastelike compound. Currently, Arctic Silver 5 is your top shelf stuff (see
www.arcticsilver.com for more details). This compound conducts heat from your chip, and transfers it into the heatsink. The heatsink is generally aluminum, and is comprised of dozens of fins, which dissipate the heat into the air around it. Optimally, there is a fan mounted directly on the heatsink to cool the fins and allow the heat to freely flow off the chip and into the surrounding air.
A basic case will have an intake bringing cool air into the case from below, and an outtake fan at the top blowing air out of the case - with your chip in the middle producing heat.
Often times, there are vents with no fans attached to them - this is due to that most manufacturers are cheap and want to minimize costs of production. This isn't good for the end user! For intake spots, that means you're not getting adequate cool air to cool the hot air coming off the heatsink, and when there's not an exhaust fan, your hot air is pooling up, which means your chip isn't getting cooled! Your fan on the heatsink is just blowing hot air at hot fins. Like I said, rule of thumb is - a fan on every vent, top ones for exhaust, bottom ones for intake.
That right there is just the facts.
Personally, I will always prefer listening to a fan going 10000 rpms than not be able to use my computer or game system. That's what good speakers are for anyways. Though, there are very high quality fans that you can get that are VERY silent, even at high rpm.
Often times, there are open chips that do get hot, yet don't even have a heatsink! You can add a heatsink to it - or even better mount a fan blowing into it too. This is a super common mod on PCs, putting a heatsink with a fan on the northbridge chip. There are also fan speed programs out there for increasing voltage to the fans. If you're feeling adventurous, you can get thermistors to regulate the voltage to the fans based on the temperature.
Cooling is a huge world with thousands of possibilities, and you're only limited by how much research you're willing to do and how deep your wallet goes.