I need help with scanning the stanza below for an assignment: "That not a worm is cloven in vain; That not a moth with vain desire Is shirvell'd in a fruitless fire, Or but subserves another's gain."

Learning how to scan poems takes practice. The first step is reading the lines aloud and hearing the alternation of weak and strong syllables as you naturally pronounce them. 
For a more analytic approach, you should start with polysyllabic words. Let's look at:

Or but subserves another's gain

Say the word "another" out loud. Try emphasizing the stress pattern. Is it "AN-oth -er", "an-OTH-er" or "an-oth-ER"? As you actually say this aloud, you will note that you naturally place the stress on the second syllable. Similarly, with the word "subserve" we naturally stress the second syllable. Now, let us consider the phrase "another's gain". Again, if you read this aloud in your natural voice, you will hear that you emphasize "gain" more than "-er". The two initial words can be said with almost any choice of emphasis; in such cases we normally mark them as following the normal pattern of the line. Thus we have:

Or BUT| subSERVES | anOTH | er's GAIN.

You will notice here that there is a regular pattern of two syllable units called "feet" each consisting of a weak syllable followed by a strong syllable. This type of foot is known as an "iamb". For each line, you can use this process to determine the relative strength of syllables.
Meters are conventionally named by an adjective indicating the dominant foot (e.g. iambic, trochaic, anapestic) and a noun indicating the number of feet in the line:
Monometer: 1 foot
Dimeter: 2 feet
Trimeter: 3 feet
Tetrameter: 4 feet
Pentameter: 5 feet
Hexameter: 6 feet
Thus, for example, a line with six dactylic feet would be referred to as "dacytlic hexameter". 
For rhyme scheme, you should look at the final words of the lines. These are:

... vain; 


 ... desire 


 ... fire,


 ... gain

If you say these aloud you will note that "vain" and "gain" have the same final vowel plus consonant sounds as do "deSIRE" and "fire". This means that we have a pattern of the first and last lines of each stanza rhyming as well as the two middle lines. This particular type of open quatrain is known as the "In Memoriam stanza". 
 
https://sites.google.com/a/ncsu.edu/morillo/