One form of the mnemonic is done by counting on the knuckles of one's hand to remember the numbers of days of the months. Count knuckles as 31 days, depressions between knuckles as 30 (or 28/29) days. Start with the little finger knuckle as January, and count one finger or depression at a time towards the index finger knuckle (July), saying the months while doing so. Then return to the little finger knuckle (now August) and continue for the remaining months.
One variant of this approach differs after reaching the index finger knuckle (July): instead of wrapping around back to the little finger, some people reverse direction and continue from the index finger knuckle (counting it for both July and August) and ending on the ring finger knuckle.
Still others use two hands (as shown in the diagram, above): starting with the little finger knuckle of the left hand, proceed to the left index finger knuckle, then (swapping hands) jump to the right fist's index finger knuckle for August, finishing on the knuckle of the right ring finger.
Lardner, Dionysius, ed. (1855). The Museum of Science and Art. 5. London: Walton and Maberly. p. 152.
When we close the hand there are four projecting knuckles of the four fingers, with depressions between them. If we give the knuckles and intermediate depressions the names of the successive months, recommencing from the first knuckle, after having once gone over them, we shall find that the months of thirty-one days are those which fall upon the knuckles.