The speaker wastes no time in stating exactly how they feel about "fame." Using a metaphor, they compare fame to a "fickle" (unpredictable or volatile) "food." Given that food is essential to life, this metaphor implies that people mustn't rely on fame for any sort of soulful nourishment.
Notice how the thick /f/ alliteration of this opening line makes the speaker's declaration all the more emphatic and memorable:
Fame is a fickle food
The first line reads like an aphorism: short, clever, and quotable, it has the feeling of bearing some profound truth in just a few words.
The speaker builds on the idea of "fame" as "food" in the next line, saying that this metaphorical meal is served "Upon a shifting plate." Not only is fame itself unpredictable, then, but the context in which fame exists is also inconstant. That is, what's in one day might be out the next; fame is "shifting" in the sense that people can never get a firm grip on it.
These first two lines are written mostly in iambic trimeter, a meter consisting of three iambs in a row, with a variation in the first foot of line 1:
Fame is | a fick- | le food
Upon | a shift- | ing plate
That opening foot ("Fame is") is a trochee (a stressed syllable followed by an unstressed syllable), which is a common variation in iambic meters and starts the poem off on a rousing, forceful note. After this, the poem follows a steady da-DUM rhythm that grants its lines a familiar, musical cadence.