As the subtitle indicates, "The Vanity of Human Wishes" is an imitation/homage to Juvenal's Tenth Satire. Both poems have a moral agenda and Johnson and Juvenal satirize the sins (i.e., pride, pursuit of wealth, greed, etc.) of their respective times.
The speaker begins the poem describing an objective or even God-like point of view. "Let Observation, with extensive view, / Survey mankind, from China to Peru;" (1-2). The speaker is indicating that this will be a comprehensive view of everything from the historical movements of nations and continents to emperors all the way down to the motivations of each individual:
Remark each anxious toil, each eager strife,
And watch the busy scenes of crowded life;
The speaker goes on to say that everyone pursues his/her hopes, fears, desires and hate. In pursuing these goals, everyone has obstacles and temptations to face en route to each of our respective fates. The "clouded maze of fate" is "clouded" because these obstacles and temptations distort our paths.
When a person chooses pride over virtue, it is as if this person proceeds without a (moral or logical) guide. Thus, the person is deluded (confused or misled) by these "treacherous phantoms" (choices which mislead).
The tenth line is a bit confusing. Basically, if one "shuns fancied ills," this seems to mean that one avoids an immoral temptation and thus, "chases airy good" meaning the righteous path.
The subsequent lines express a skeptical outlook; that is, to say it is rare that people and nations make reasonable, ethical, or "good" choices. The rest of the poem is similarly skeptical in its satire but the end does offer some hope.