How many feet are in each line of "The Dream" by John Donne?

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.