Find the key signature: It is located immediately after the bass or treble clef. It will be a good indicator (though not totally failsafe) as to the key of the song.
Count the flats and sharps:
Sharps look like the numerical pound sign (#). Flats look like a lowercase b.
If a key signature has no flats or sharps, the piece is more than likely in the key of C. Sometimes, depending on the person who wrote the sheet music, a song will be transcribed in a key different from the one in which it was recorded or performed.
Decode the key signature:
One sharp = Key of G (E minor)
Two sharps = Key of D (B minor)
Three sharps = Key of A (F# minor)
Four sharps = Key of E (C# minor)
Five sharps = Key of B (G# minor)
Six sharps = Key of F# (Eb minor)
One flat = Key of F (D minor)
Two flats = Bb (G minor)
Three flats = Eb (C minor)
Four flats: Ab (F minor)
Five flats: Db (Bb minor)
Six flats: Gb (Eb minor)
Listen to the song: If this is a previously recorded piece of music, listen to a few measures and pick out the main note -- the one that seems to hold the whole thing together, the one that would fit if it were played continuously throughout the whole song.
Know the first note or chord: In most popular Western music, the first note or chord is a giveaway as to the key of the song. If you can identify this note, you can more than likely identify the key.
Play a bit: If you're still having trouble, pick up a guitar or sit down at the piano and run through the Ionian major scale. (Do Re Mi Fa So La Ti) Find out where the scale works, and identify the first note. That note is more than likely the key of the song.