To work out the meter of a poem, first count the number of syllables in a line. If this varies greatly from line to line, the poem may have no regular meter, but if each line has a set number of syllables, or there is only slight variation, the verse is likely to be metered. Once you have counted the syllables, try to work out which are long, or stressed, and which are short, or unstressed. This becomes much easier with practice.
By far the most common rhythm in English poetry is iambic. In fact, this is so prevalent, that it is worth automatically trying to see if a poem fits into the iambic meter before considering others. An "iamb" consists of two syllables, the first short or unstressed, the second long or stressed. It is sometimes spoken or even written as "di-dum," with "di" standing for the short/unstressed syllable and "dum" for the long/stressed one. A line of eight syllables in which there are four iambs is known as iambic tetrameter. One with ten syllables and five iambs is iambic pentameter. These are the most common meters. Here is an example of iambic tetrameter:
If all the world and love were young
di-dum di-dum di-dum di-dum
Here is one of iambic pentameter
Shall I compare thee to a summer's day
di-dum di-dum di-dum di-dum di-dum
The majority of English metered verse is covered by these two meters. Sometimes one encounters fewer iambs (a line with two would be an iambic dimeter and with three a trimeter) or more (six in a hexameter, seven in a heptameter). At other times, the verse is not iambic. The next most common arrangement of syllables (which is known as a "foot") is the trochee (dum-di). This is used by Edgar Allan Poe in "The Raven."
Once upon a midnight dreary
dum-di dum-di dum-di dum-di
This is a line of trochaic tetrameter. If you say it to yourself, it is immediately apparent that it will not fit into the smoother iambic rhythm. Once you have accustomed yourself to identifying which syllables are long/stressed and which are short/unstressed, you will be able to spot more unusual "feet" such as the spondee (dum-dum) and the three-syllable dactyl (dum-di-di). These are rare in English poetry but common in Latin and Greek.