The easiest way to talk about metrical feet is to explain it in terms of cadence, or the "beat." If you try to read the poem slowly, you will find that it has a series of predictable "ups" and "downs," places where you stress and don't stress certain syllables. Most poems that do have a predictable cadence have a pattern for every two syllables. (There are some more complex patterns, such as poems that have three syllables per foot, but I'll just mention that here for future reference.) This poem does have a cadence of stressed and unstressed syllables for every two syllables.

If you have a hard time finding those divisions, I would recommend saying the poem aloud and clapping out the syllables, drawing a line after every two claps. You'll notice that sometimes you divide a foot between words and sometimes you have to divide the foot in the middle of a word. Either way is fine. Here is how I would divide this poem into metrical feet, with l identifying the breaks between feet:

Dear love, l for noth l ing less l than thee
Would I l have broke l this hap l py dream;
It was l a theme
For reas l on, much l too strong l for fan l tasy,
Therefore l thou wak'd'st l me wise l ly; yet
My dream l thou brok'st l not, but l contin l ued'st it.
Thou art l so true l that thoughts l of thee l suffice
To make l dreams truths, l and fab l les his l tories;
Enter l these arms, l for since l thou thought'st l it best,
Not to l dream all l my dream, l let's act l the rest.

As light l ning, or l a tap l er's light,
Thine eyes, l and not l thy noise l wak'd me;
Yet I l thought thee
(For thou l lovest truth) l an an l gel, at l first sight;
But when l I saw l thou sawest l my heart,
And knew'st l my thoughts, l beyond l an an l gel's art,
When thou l knew'st what l I dreamt, l when thou l knew'st when
Excess l of joy l would wake l me, and l cam'st then,
I must l confess, l it could l not choose l but be
Profane, l to think l thee an l y thing l but thee.

Coming l and stay l ing show'd l thee, thee,
But ris l ing makes l me doubt, l that now
Thou art l not thou.
That love l is weak l where fear's l as strong l as he;
'Tis not l all spir l it, pure l and brave,
If mix l ture it l of fear, l shame, hon l our have;
Perchance l as tor l ches, which l must read l y be,
Men light l and put l out, so l thou deal'st l with me;
Thou cam'st l to kin l dle, goest l to come; l then I
Will dream l that hope l again, l but else l would die.

The trickiest part of the line divisions is definitely dealing with the words with apostrophes. Those words are also pretty archaic for modern English, so it can be tough to figure out how you might say words like "cam'st" or "thought'st." But if you look at the overall pattern, you'll see that the poet means for those to be combined into one syllable together.

John Donne's "The Dream" takes an unconventional approach to meter. Usually, in traditional English poetry, the poet will consistently adopt the same meter across every line of the poem. So, for example, for poems written in iambic pentameter, every line will contain five iambic feet (see Favoritethings' answer for a definition of what this approach to meter entails). Similarly, a poem written in iambic tetrameter would contain four iambic feet, iambic hexameter six iambic feet, etc.

What's interesting about this particular poem is that it cycles between three different metric styles (and it does this in a consistent underlying pattern). The poem is divided into three stanzas, and the first two lines of each stanza is always written in iambic tetrameter. However, then we come to the third line of each stanza, which is iambic dimeter (two iambic feet). Then the fourth line reads in iambic pentameter, the fifth line returns to iambic tetrameter, and the rest of the stanza is all in iambic pentameter. Each stanza is organized in that same metric structure. Even so, it looks a little tricky in the second stanza, whose fourth and fifth lines read as follows:

(For thou lovest truth) an angel, at first sight;
But when I saw thou sawest my heart

I suspect that for the purposes of the poem, the words "lovest" and "sawest" should be read as half a foot (in these cases, your iambic feet would read "lovest truth" and then "thou sawest"). Otherwise, the meter breaks down entirely.

Regardless, the entire poem features that same underlying structure across all three stanzas. It cycles between Iambic Tetrameter, Iambic Dimeter, and Iambic Pentameter. That is, some lines feature four iambic feet, others two iambic feet, and still others five.

This poem is written in a meter called iambic tetrameter, and this means that there are four (tetra-) metrical feet per line. The metrical foot is called an iamb (where we get "iambic"), and this means there are two syllables per foot: one unaccented syllable followed by one accented syllable. The typical line in the poem, then, will have eight syllables. I will mark up some lines below so that you can see where the feet begin and end and which syllables are accented:

Dear love | for no | thing less | than thee |
Would I | have broke | this hap | py dream |

Each "|" marks the end of a foot, and each word or part of a word appearing in bold is the accented syllable of that foot.  If the meter were dimeter, there would be two feet per line; trimeter would have three feet per line; tetrameter (like this poem) has four feet per line; and pentameter has five feet per line. Tetrameter and pentameter are the most common meters used in English language poetry.