An accidental is a sharp, flat, or natural sign that is not in the key signature but appears next to a note. Accidentals only last until the end of the measure or through tied notes across a measure.
In the key signature sharps and flats always appear in the same order which is directly related to the circle of fifths.
Order of sharps: F C G D A E B
Fat Cats Gargle Daily After Eating Breakfast. Yea I know it doesn't really make sense, but it really helps you remember the order of sharps.
Order of flats: B E A D G C F
I never really had a saying for this one, I just remember Bead GCF. But I suppose you could use Before Eating At Dennys Guys Can Fart.