Condensers channel light from the light source into a cone directed through the sample. Located below the stage on a regular compound microscope, condensers are generally less diverse than objectives regarding their features and interchangeability, but there are a few types that are worth being aware of:

Abbe Condenser
The Abbe condenser is the most common type of light microscope condenser, usually a standard on all new budget and most used microscopes. An Abbe condenser generally consists of two lenses to direct light through the sample.
Common components on an Abbe condenser include: an iris diaphragm, a shutter-like slider with a lever to control the amount of light let into the condenser, known as aperture. A flip-top lens, othewise known as a flip-out or swing-out condenser, allows the top lens to be moved out of the way, meant for use with lower magnification objectives to broaden the cone of light passing through the slide, illuminating the whole sample rather than just the centre. Finally, a filter holder is found on some condensers, holding filter discs/lollipop filters for different techniques.

Corrected Condensers
Just like objectives, condensers can possess optical correction, either for chromatic or spherical aberration. A condenser which only corrects for spherical aberration is known as aplanatic, a condenser which only corrects for chromatic aberration is known as achromatic, and a condenser which corrects for both is, you guessed it, aplanatic-achromatic. 
While a condenser can be corrected, it is not common to see this on hobby microscopes simply due to expense.

Phase Contrast Condensers
Phase contrast setups require specialised phase contrast condensers possesing an annulus and phase plate. I do not know enough about phase contrast to explain any further in detail here, sorry!

Condenser Controls
Condensers come in all different shapes and sizes, but their basic functions and controls always remain the same. 
Looking at the diagram on the bottom right, different parts and their functions will be displayed here:

Iris Diaphragm: Used to control the amount of light entering the condenser
Centering Knob: Used to center the condenser, so the beam of light is passing directly through the centre of the stage opening.
Lens: The bit light goes through.