Examine the key signature. Sharp key signatures have sharp signs that look like pound signs ("#") to the right of the treble or bass clef. Identify the note with a sharp furthest to the right of the key signature.
Identify the note one step up from this sharp sign. In other words, if the sharp sign is on a line, go to the note on the space above it; if the sharp sign is on a space, go to the note on the line above it.
Determine whether or not this note has a corresponding sharp in the key signature. If not, the note by itself is the correct major key. If it does have a corresponding sharp, than the note plus "sharp" is the name of the major key ("A sharp," for example)
Identify the note one step down from the rightmost sharp sign.
Repeat step 4 for this note. This is the name for the minor key that the key signature corresponds to.
Examine the key signature in question. If it is a flat key signature, there will be flat signs (these look like lowercase "b"s) to the right of the treble or bass clef. Find the flat furthest to the right of the treble or bass clef.
Find the note three steps down from this flat.
Determine whether or not the note identified has a corresponding flat in the key signature. If not, the note by itself is the correct name of the major key. If it does have a corresponding flat, than the note plus "flat" is the correct name of the major key.
Identify the note two steps up from the rightmost flat sign. Repeat step 4 for this note. This is the minor key that the key signature corresponds with.