Listen to a couple of measures of the song, then count to the beat: “ONE, two, three, four, ONE two, three, four.”
Place your index finger on the first fret of the sixth string -- the highest, thinnest string -- the E string. Strike that tone – the note F -- on the “ONE” beat of the next measure. Critically listen to the tone to see if it sounds good with the song, or if it is sharp, flat or harsh.
Move your finger up a fret to F sharp. Strike that tone on the ONE beat of the next measure. Let the note ring while you critically listen again to see if it is discordant.
Continue moving up the fretboard striking each tone: the G of the third fret, the G sharp of the fourth fret, the A of the fifth fret, the B flat of the sixth fret, the B of the seventh fret, the C of the eighth fret, the C sharp of the ninth fret and the D of the tenth fret.
Choose the tone that sounds the best to your ear to play again. Strike that note, holding the string down with your index finger.
Depress the same string two frets up from that tone with your ring finger on the third beat of the measure. Pick back and forth from the original tone and the new one by keeping your index finger on the original tone and lifting and replacing your ring finger. For example; if the A note of the fifth fret is one of the ones that sounds good, alternate playing it with the B of the seventh fret.
Discard the original tone as the name of the scale you are looking for if the second note doesn’t sound good. Move further up the fretboard, testing a different note from the ones that sounded good and the one two frets above it.
Play a note two frets above the second tone when you find a two-note combination that does not sound discordant with the song. For example; if the original note is A at the fifth fret and the second note is B at the seventh fret, try the C sharp at the ninth fret. If that note doesn’t sound good, try the note two frets below the original note.
Name the scale the lowest note of the three-note combination. For example; if the A, the B and the C sharp sound good, the scale is A. If the C sharp does not sound good, and you had to try the G of the third fret, and the combination of G, A and B sounds good, name the scale G.