I happened to acquire a small version (a microcentrifuge, or microfuge), and this is how I use it.
Caveat: I'm not saying this is the correct way to use a microfuge, since I have never had any actual training in same, there does not seem to be much in the way of advice online, and manufacturers I have contacted have decided not to respond to my requests for advice (after all, who is going to be in the position of acquiring a piece of delicate laboratory equipment without acquiring the appropriate skills? Apart from me, I mean.)
Step 1: What is a centrifuge?
Through centripetal forces, this subjects the sample to artificially-high "gravity" (actually acceleration, but it amounts to the same thing), often thousands of times the gravity acting on you as you read these words.
It is exactly the same effect you exploit when you spin a bucket of water over your head - if the water wasn't subjected to slightly over one gravity of acceleration ("1g"), then it would pour out of the bucket and all over you.
Sinking and Floating
As you already think you know, heavy things sink and light things float. To be more accurate, denser substances tend to sink in less dense substances. If the difference is great enough, and the particles large enough, the sinking happens at visible speeds, say stones in water.
However, if the particles are very small, or the difference in densities is very slight, or the liquid very viscous, then the sinking can be infinitesimally slow, or even non-existent. The perpetual, random motion of the particles of liquid can constantly re-mix the solid into the liquid, or the liquid's viscosity can simply trap particles and hold them in suspension.
Increase the gravitational forces, though, and even tiny differences in density can be exploited to separate mixtures into layers. That is what a centrifuge does - it uses centripetal forces to increase the apparent gravity acting on the sample, which makes things sink or float more quickly.
Centripetal versus Centrifugal.
We often talk about centrifugal force that pushes things outwards as they spin. This is an intuitive concept (after all, we can feel the force pushing us sideways when we corner in a car), but it is wrong.
But let us remind ourselves of Newton's First Law of Motion:
Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
What? Your Latin's a bit rusty? OK:
Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
That is - nothing changes speed or direction unless there's a force acting on it.
So, for our high-speed sample to curve away from it's straight line into the circle of the centrifuge, there has to be a push from the outside or a pull from the middle. Since there is nothing outside the circle, it must be the pull.
The forces involved
There is a simple calculation for the g-forces generated by a centrifuge:
RCF = 0.0001118rN2
RCF = Relative Centripetal Force (the "g" forces exerted)
r = the radius of the centrifuge in centimetres
N = the rotational speed (revolutions per minute)