There are several different types of ink reservoir systems used with fountain pens - but for the simple fact that the majority of today's pens are mostly made for cartridge ink refills, I will only discuss this type in this article.  But, you can also refill your fountain pen ink from a bottle, which usually you have more color options this way and it's much more economical and "eco" freindly too.

To do this you can use what's known as a Converter. Twist the end of the converter counter-clockwise until the piston head is positioned at the filling end. Press the converter onto the nipple of the feed.  With the nib submersed in the (bottle of) ink, twist the end of the converter clockwise until it fills with ink and stops.  Completely twist the end of the converter back and forth a few times to be sure it is completely filled.  Now, gently twist counter-clockwise and allow two drops of ink to drip back into the bottle.  Remove excess ink from the nib with a paper towel.