The original question was how to play grace notes. I am not sure it is helpful to bring in accidentals, since grace notes may or may not be accidentals.
As Ken notes, grace notes are often ornamental in nature and not an essential part of the melody. As Robin explains they are usually written much smaller than regular notes in standard musical notation.
Grace notes always appear just before a note and they receive no counted value. The note just after the grace note sounds on beat, so the grace note actually takes away some of the duration of the note preceding it.
On a stringed instrument, a grace note would be plucked with the right hand, but the left hand would employ a slide, a hammer-on, or a pull-off to play the main note after the grace note. I do not think many of us could actually pick both notes fast or smoothly enough. But the important point, again, is that the note following the grace note falls exactly on the beat, so the grace note precedes it without itself receiving any counted value.
Below is the first line of my arrangement of the old Quaker hymn Beech Spring. Notice the three grace notes. In each case, I suggest playing it as a hammer-on. If this were arranged for noter/drone play in DAA, I would suggest a slide in the first case and a hammer-on in the second and third since the grace note would be the open string. And note that none of these grace notes are accidentals.
Dusty T., Northern California
"A good song makes you laugh, it makes you cry, it makes you think."
-- Pete Seeger
updated by @dusty-turtle: 05/11/16 05:37:33PM