The button filler has a small button (brass or aluminium or occasionally plastic) on the end of the barrel under a small "blind cap".  Pressing the button compresses the ink sac via a sprung pressure bar.  Filling is the same as for a lever filler.  To fill you simply press the button fully, immerse the nib in ink and then release the button.  You need to wait several seconds to allow the ink to be drawn up.  Now lift the pen out, shake any surplus ink off gently and wipe the nib with a tissue.  Done!  It is not necessary to operate the button more than once.