tetrameter is a line with four feet. The more common type of verse is iambic pentameter, which has five feet, each with an unstressed syllable followed by a stressed syllable. Iambic pentameter is a relatively natural meter form in English, and many poems and plays are written in this type of meter.  

The rhyme scheme for this poem is ABABCC. That is because the first line ends with "grace," and the third line ends in "face." The second and fourth lines end with "deed" and "bleed," and the last two lines (referred to as a couplet) end with "dropped" and "stopped." This type of rhyme scheme is called an English sestet, and it was originally a Sicilian rhyme scheme that was popularized by Shakespeare in his sonnets. 

To help you get started on this assignment, let's take a close look at the poetic technicalities in the third stanza of Robert Browning's “Count Gismond—Aix in Provence.” The stanza is written in iambic tetrameter. This means that there are eight syllables in each line, two per each of the four poetic feet. The syllables follow the pattern unstressed-stressed.

We can take the stanza's first line as an example: “I thought they loved me, did me grace.” If we rewrite the line putting the stressed syllables in bold, we get this: I thought they loved me, did me grace. Each pair of unstressed and stressed syllables makes a poetic foot, so “I thought,” “they loved,” “me did,” and “me grace” are the four feet in this line. This is in iambic meter because the unstressed syllable comes before the stressed syllable.

The rest of the stanza's lines follow suit in this iambic tetrameter, but as you scan them, remember that often times one syllable in a two-syllable word may be stressed while the other is unstressed (“showing” in the third line, for instance).

As for the rhyme scheme here, we notice that the stanza follows the pattern ababcc. The words “grace” and “face” are the a rhyme, “deed” and “bleed” the b rhyme, and “dropped” and “stopped” the c rhyme.

In order to determine the meter of a poem, you must first read the lines and pay attention to which words or syllables are stressed, or ACCENTED.  In order to do this, read aloud and listen to where the natural stresses fall; identify the stress of multiple syllable words by using a dictionary to identify stress, or accent.  I have bolded the stressed (accented) syllables in the lines below:

I thought they loved me, did me grace
To please themselves; 'twas all their deed;
God makes, or fair, or foul, our face;
If showing mine so caused to bleed
My cousins' hearts, they should have dropped
A word, and straight the play had stopped.

Once you have the stressed, or accented, syllables marked, then you need to look for the pattern established.  In this case, you can see the da DUM da DUM pattern.  This pattern helps you to identify the metrical rhythm. This rhythm is called an iamb, which is an unstressed syllable followed by a stressed syllable.  Next you count how many repetitions of the pattern appear in each line of the poem.

In this case, there are 4 repetitions of iambs per line, which means that this poem is a tetrameter: four repetitions of a patterns.  The meter of the poem is a  two-part name created by the identification of the predominant rhythm, which is iambs, and the number of repeated feet per line. That means this poem is in iambic tetrameter. You can learn more about the various metrical feet by reviewing the links below.

The first tactic you should use in scanning a poem is to look for words containing more than one syllable. Start with the line:

If showing mine so caused to bleed

The word "showing" can only be pronounced one way, showing (NB: the bolded syllable is stressed). Say it out loud. Try pronouncing the word first as showing and then as showing, and it will be obvious that the word must be stressed on the first syllable. 

This then gives us the first clue as to how to scan the line. Next, think about the word "if." It is a small, monosyllabic word, and probably less important than the verb "showing" and thus we would not be likely to stress it in reading. So far, we have:

If showing mine ...

Next, you should look at the other words in the line and read them aloud. In general, small, unimportant words such as conjunctions and prepositions are naturally unstressed and more important words such as nouns and verbs stressed. Thus one would say "to bleed" rather than "to bleed".

Thus the line would be scanned:

If showing mine so caused to bleed

You can see a regular pattern of an unstressed syllable followed by a stressed syllable (thus the basic foot of the line is iambic) repeated four times (thus the line is a tetrameter). The meter of the line therefore is iambic tetrameter. The lines you quoted all follow the identical pattern of regular iambic tetrameter. The rhyme scheme is ABABCC.