To answer this question, you may first need to fully understand the meaning of the word fate. Fate is a person's destiny, something that inevitably happens to person. For example, we can say that we are all fated to die. Death is an avoidable part of human nature. Once you understand the meaning of the word fate, you can then go back through the play and find places in the play where the words "stars," "potions," "the sun and the moon," or "larks and nightingales" are used. Once you've found passages containing these words, it will be easy to see how the words are being used and whether or not they relate to fate.
For example, "larks and nightingales" are mentioned in Romeo and Juliet's wedding night scene. Early in the morning, when Juliet sees that Romeo is getting ready to leave, Juliet argues, "Wilt thou be gone? It is not yet near day. / It was the nightingale, and not the lark" that he heard (III.v.1-3). Nightingales are special birds that only sing at night, while larks sing in the morning. Hence, if it was the nightingale singing rather than the lark, then that's a clue that it is still nighttime and not early dawn; therefore, Romeo could stay a little longer. Since this passage has nothing to do with fate, we know that nightingales and larks are not symbolizing fate, but rather morning and night.
"Potions" is also an easy word to look up. Potions are only mentioned a couple of times in the play. The first time is when Friar Laurence gives Juliet a potion that will make her look like she is dead. The second time is when, believing that Juliet is truly dead, Romeo purchases a deadly potion so that he can drink it and die by Juliet's side. Since, again, fate is not mentioned in either of these parts, we know that potions are not symbolizing fate, but rather death.
References to the "sun and the moon" are frequently seen. We especially see these words used in the famous balcony scene. Romeo compares Juliet to the sun in the line, "It is the East, and Juliet is the sun!" (II.ii.3). He also later compares Juliet to the moon, saying that she is far more beautiful than the moon. Hence, again, since fate is not mentioned in this passage, we know that the sun and moon are not symbolizing fate, but are rather analogies being used to describe Juliet's beauty.
Stars are also frequently mentioned. The first time we see the word stars used is when Romeo proclaims his premonition that crashing the Capulets' ball will bring awful consequences, as we see in the line, "...for my mind misgives / Some consequence, yet hanging in the stars" (I.iv.113-14). Consequences, especially unavoidable consequences, are a part of fate. A second time we see the word stars being used is when Romeo learns about Juliet's death and exclaims, "Is it e'en so? Then I defy you stars!" (V.i.24). What Romeo is saying here is that he is defying his own fate. Hence, since both of these lines refer to fate, we know that it is stars that are being used to symbolize fate.