Do the counting first — the shape of the stanza is what makes the stresses predictable.
Syllable count, every stanza: line 1 = 8, line 2 = 6, line 3 = 8, line 4 = 6.
With the rhyme scheme abab, that 8-6-8-6 pattern is called common metre — the metre of ballads and hymns.
The beat you hear when the poem is read aloud is iambic — an unstressed syllable followed by a stressed one, te-TUM, four times in the long lines and three times in the short ones. Marked with bold for the stresses:
If WORDS could SAt-is-FY the HEART,
The HEART might FIND less CARE;
But WORDS, like SUM-mer BIRDS, de-PART,
And LEAVE but EMP-ty AIR.
The HEART, a PIL-grim UP-on EARTH,
Finds OFT-en, WHEN it NEEDS,
That WORDS are OF as LIT-tle WORTH
As JUST so MAN-y WEEDS.
A LIT-tle SAID, and TRU-ly SAID,
Can DEEP-er JOY im-PART
Than HOSTS of WORDS, which REACH the HEAD,
But NEV-er TOUCH the HEART.
The VOICE that WINS its SUN-ny WAY,
A LONE-ly HOME to CHEER,
Hath OFT the FEW-est WORDS to SAY;
But, OH! those FEW, how DEAR!
If WORDS could SAt-is-FY the CHEST,
The WORLD might HOLD a FEAST;
But WORDS, when SUM-moned TO the TEST,
Oft SAT-is-FY the LEAST!
Like PLANTS that MAKE a GAUD-y SHOW,
All BLOS-som TO the ROOT;
But WHOSE poor NA-ture CAN-not GROW,
One PAR-ti-cle of FRUIT!
A note on the example printed in your book. On page 224 the underlines fall on If, could, tis / The, might, less / But, like, mer, de / And, but, ty — that is, on the odd-numbered syllables (1st, 3rd, 5th, 7th). Read the lines aloud and you will find the beat falls the other way, on the even-numbered syllables, giving the te-TUM of common metre. Follow your teacher’s reading, since that is what the exercise asks you to do; but if your marking comes out as above, you are hearing the poem correctly.
What the metre is doing for the poem. Common metre is the beat of hymns and ballads — plain, public, easy to remember, the rhythm of something meant to be spoken to other people rather than admired on a page. That is a pointed choice for a poem which argues that the best speech is short, plain and true. Notice too where Swain breaks the beat: “But, oh! those few, how dear!” has an extra pause after ‘oh’, and the line stumbles for a moment — exactly at the point where the poem stops arguing and simply feels something.