Metaphor is one of the most common figures of speech, and Browning uses several in this poem:
"'I lover her for her smile ... her look ... her way Of speaking gently, ... for a trick of thought That falls in well with mine [...]" (lines 3 to 5)
The speaker imagines the lover saying that she has "a trick" (characteristic manner) of thought which "falls in well" with his own. By choosing to use the phrase "falls in well" instead of "goes well with," Browning is comparing the act of "getting along" to "falling down." When you look in the dictionary (see resources) you will see that the verb "to fall" has several negative denotations, such as "to yield to the control of enemy forces," and you might wonder what kind of relationship the lover has in mind.
Take a look at lines 13 and 14:
"But love me for love's sake, that evermore Thou may'st love on, through love's eternity."
Here, Browning uses hyperbole (or exaggeration) not only in sentiment, but also in word choice. "Evermore" (literally meaning "forever") and "eternity" are, in most applications, hyperbolic or exaggerating words. As well, the speaker's wish that the lover love her until the end of time is not possible. The unreality of this proposal might lead you to believe that, perhaps, the speaker's request is not sincere, or at least not realistic.
Alliteration involves the repetition of consonant sounds not only at the beginning of words, but -- more importantly -- at the beginning of their stressed syllables. "Sonnet 14" provides a good example of this in line 2:
"Except for love's sake [...]"
Note that the word "ex-cept" is stressed on the second syllable, and that syllable has the same initial "s" sound as "sake." The repetition of this hiss-like sound might remind of you a snake, which has a reputation for being devious. (Tip: Use your dictionary to find out which syllable is stressed in a word.)
By analyzing plays on words -- puns -- you can add deeper meaning to the poem and often generate a variety of readings. For instance, in lines 11 to 12,
"A creature might forget to weep, who bore Thy comfort long [...]"
If you think about Browning's choice of the word "bore," you will realize that it has several meanings. The primary meaning of bore is "to support the weight of," but it can also mean "to endure," which may put a negative spin on how the speaker feels about the lover.