Use an acronym to help you learn the names of the notes that fall on the lines of the grand staff. The grand staff includes both the treble and bass clef (see ref, 1). Use Every Good Boy Does Fine to learn the names of the notes on the lines in the treble clef and FACE to learn the notes between the lines. For the bass clef, use Good Boys Do Fine Always, and All Cows Eat Grass for the notes on the lines and between the spaces. You can also make up your own acronym if you want to be creative.
Print a copy of a circle of fifths chart. The circle of fifths chart shows the pattern of sharps and flats in a key signature. View the circle of fifths chart and you'll notice that a sharp is added when moving clockwise and a flat is added when moving counter-clockwise. For a printable circle of fifths chart see the resource section.
Look at the last accidental in the key signature to determine the major key. If the last accidental is a sharp sign, move up one space on the grand staff to get the major key. Look at the second to last flat in the key, if it contains flats. The line or space that the penultimate flat falls on will be the major key. There are a few exceptions which you will have to memorize. If there are no accidentals, then the key is C major and if the key has one flat, then it's F major.
View the circle of fifths chart to find out if the key signature is a major or minor one. Once you've found the major key in the previous step, look at the circle of fifths chart. You will see that each major key has a relative minor. For example, the relative minor of "C" major is "a" minor. Look at the last chord or note in the sheet music. Check if it corresponds to the major key or the relative minor key in the circle of fifths.