This is a subject area that confuses a lot of students --  unecessarily.  It is fairly simple as an idea, and with a degree of practice, easily applicable.

First let´s talk about meter.  The word meter (or in British English metre) simply indicates, as its origins suggest, a measurement of some kind.  With any kind of meter, whether it is a gas meter, a water meter, or poetic meter, one needs to understand is what is being measured and how (in what kind of unit of measurement).  Poetic meter deals in units of set rhythms, called feet.   When one find the rhythms, one measures those rhythms according to their patterns, sequences or groupings (see common patterns of metrical feet below).

Again, the descriptive language of meter can be confusingly alien.  But it is really just a matter of learning the names of fairly simple concepts.  The underlying rhythms that one measures in poetry are binary.  Meter is a made up of patterns of stressed and unstressed sounds in poetry, sometimes the pattern is obvious and apparent, sometimes it is broadly interpretive.   

This has further implications, inevitably.  Some students take the opinion that meter is very much a personal read (i.e. any interpretation of poetic meter is correct because this whole thing of stressed and unstressed words is an inexact science).  While there is a germ of truth in such an idea (some poetry does indeed invite conflicting readings), the assumption that one can read poetry any which way is basically wrong.  For example, most words are not "open to interpretation" they have instrinsic stresses (relative) built into them so that pronunciation is not a matter of choice:

Alongside the inherent or natural pattern of stresses occuring in words themselves, are the common rhythms of stressed and unstressed syllables that poets use as the beat or music of their poetry.  These rhythms are commonly identified both by the name  and notation of the metrical foot (see the chart below).  The notation doesn´t migrate very comfortably to keyboard symbols, traditionally being a "/" to indicate a stressed, or relatively heavily stressed syllable, and something between a "u" and a "-" to indicate an unstressed syllable.  For the sake of convenience (and so as not to cause confusion where I´ve separated syllables using hyphens, unstressed syllables are designated with a "u" below).

Some students often seem heavily resistant to the idea that poets, rather than professors, use these terms or incorporate these concepts/formal rhythms into their work.  Perhaps poetry is more alluring if it seems to spring organically and fully formed, like aphrodite, from the creative genius of a poet, rather than being put together with clockwork and springs and rhetorical devices galore, but such a romanticised view of the writing process is generally far from the truth of the way most poets work.

While the merits of the following poem are debatable, this playful excerpt from Coleridge´s "Metrical Feet" at least makes very clear the poet´s familiarity with meter and rhythm in his aggressive and humorous combination of form and function (and a few instances of  forced or strained meter):

The other part of the equation that one needs to be familiar with, alongside the ability to identify  patterns of rhythms (metrical feet), is to be able to measure the sequences, or duration, of those patterns.  So the language of measurement, of poetic meter, is generally made up of the kind of metric foot + the number of rhythmic units in a given line of poetry. 

Iambic poetry, for example, is very common (probably the dominant metric form  in English poetry -- and closest to the "natural" intonations of speech -- if there is such a thing).  Generally, if one describes the presence of iambic feet in the meter of a poem, one also describes how many feet are present in a line.  Shakespeare´s sonnets, for example generally consist of five iambic feet, or iambic pentameter:

The measurement of feet in a line is simple, as long as you can identify the kinds of metric feet (rhythms) being used.  It is only obliquely concerned with syllable count.  Iambic pentameter will have 10 syllables in a given line (2 x 5, as above), while anapestic pentameter (3 x 5) will have 15.  Note that some poetry (like some of Dylan Thomas´s, for example), rather than being organized according to meter is organized instead by syllabics, where the syllable count, rather than the pattern of stresses is the dominant organizing feature.