Identify the major (also known as the Ionian) scale. It has half-step intervals of 2, 2, 1, 2, 2, 2 and 1 so the notes in the A major scale are A, B, Db, D, E, Gb, Ab and A.
Examine the corresponding Mixolydian scale. It consists of the same intervals of notes in Step 1 except it begins on the fifth note of the major scale. The Mixolydian scale therefore has intervals of 2, 2, 1, 2, 2, 1, 2.
Observe that the Mixolydian scale is therefore the same as the major scale of the same key except the seventh note is flattened, giving you A, B, Db, D, E, Gb, G and A for the key of A.
Learn the Mixolydian scale in all positions. There are generally five patterns (plus a sweep pattern) for the Mixolydian scale with the second position probably being the most common.
Play the Mixolydian scale in A with the second position as follows: 6-5-M, 6-7-P, 5-4-I, 5-5-M, 5-7-P, 4-4-I, 4-5-M, 4-7-P, 3-4-I, 3-6-R, 3-7-P, 2-5-I, 2-7-R, 2-8-P and 1-5-I. The first digit is the string (6 being the lowest), the second digit is the fret and the letter provides the fretting finger (I for index, M for middle, R for ring and P for pinkie). The first note in the example is 6-5-M, meaning that the middle finger frets the sixth string at the fifth fret.