Meter in poetry is a lot like time signature in music. If you can read music, you can figure out poetic meter! In order to show the meter, I am capitalizing the syllables that are stressed in each line. What you will notice is that in each line, two patterns emerge.
There WAS a young LAdy of WILTS
Who WALKED up to SCOTland on STILTS...
She ANswered, "Then WHAT about KILTS?"
The first pattern that you notice in each line is in the first two syllables: an unstressed syllable followed by a stressed (there WAS... who WALKED... she AN). If you were to bang the rhythm of each line on a desk, the second syllable would get the beat. This pattern is called an iamb.
The second pattern you will see in each line is a three-syllable pattern, and the pattern is repeated (a young LA... dy of WILTS, up to SCOT...land on STILTS, swered, "Then WHAT...about KILTS?"). In each case, the THIRD syllable gets the beat while the first two are unstressed. These are called anapests.
The SOUND for each line is as follows:
da DA da da DA da da DA (or for those who wish to use numbers) a ONE and a TWO and a THREE
Since the most prominent poetic foot is the anapest (the one used most frequently throughout the poem), then the meter is considered anapestic. Three beats is TRImeter. Limericks are mostly anapestic trimeter.
I hope this is not too confusing!