It varied. Mostly the early inductees into polygamy were leaders in the early church and close confidants of Smith. Most of the rank and file members were not aware that polygamy was even taking place while Joseph was still alive. And Joseph was giving public speeches denouncing the practice right up until his death.

Among the leaders who were introduced to the doctrine reactions were... mixed. On one side you had leaders like the Apostles Brigham Young, Orson Hyde, Orson Pratt, Parley Pratt, Heber Kimball, and others who all took on additional wives. And several of whom allowed Joseph to marry their wives.

On the other side you had early leaders like Oliver Cowdrey (the second elder of the church after only Joseph) who was excommunicated for calling Joseph's first plural marriage, "an ugly, dirty, nasty affair," and calling him out as an adulterer. Likewise his two assistants and close advisors Sidney Rigdon and William Law both opposed the practice. And both refused to allow Joseph to marry family members. Law even started a rival church. He also started a newspaper to reveal what was happening to the rank and file members. Joseph's arrest and eventual murder can be tied to his illegal destruction of the paper's printing press.

QuickSpore's responses are quite good, but I would introduce a few caveats because it's a complicated question.

First: widespread adoption of the practice took place long after Smith's death. The church only began officially sanctioning it in 1852, five years after the LDS exodus to Utah and eight years after Smith's death. Prior to the official sanctioning, it took place in secret amongst the church elite and was a source of a lot of consternation. Even many of the elites who practiced it record initial feelings of confusion or revulsion, and it inspired Law to depart the church (again, noted above).

Second: It is very difficult to pin down when Smith "introduced" the practice. Basically, as we go through the years of Smith's life, we get a higher and higher probability that Smith has introduced it in secret, butt it's difficult to be certain because, well, it was secret. Certainly by Smith's death he had stirred up enough controversy over it that it is nearly impossible to imagine that the practice wasn't coming from him, even though he vociferously denounced plural marriage right up to the end (in public).

Third: the problem of that secrecy is exacerbated by the allegations of sexual impropriety that haunted the church throughout its early period. That's tied into the way new religious movements of the period were perceived by broader American culture. Basically, most Americans, especially the famously prudish New Englanders who surrounded the early Mormons, drew connections between religious revivalism and a certain looseness of sexual mores. This was exacerbated by the presence of powerful woman figures, such as Emma Smith (or Ann Lee of the Shakers, for another example), and was used as a way to discredit new religious movements of the time. Thus, early Mormons had significant incentive to resist any allegations that there was anything divergent about their beliefs on sex and the family. This means that even if Smith felt revelation compelled him to engage in plural marriage as early as the 1820s (for which there is some evidence), the weakness of the church's position (and his own) would discourage him from admitting it, and it isn't like we have a lot of access to the private thoughts of semi-literate farmers from the early 1800s.

Lastly, I'll note that the most significant schism in the history of the various religious movements surrounding Smith centers on precisely this issue. Emma Smith, by all accounts, did not approve of plural marriage, and her reaction(s) to it ranged from look-the-other-way denialism to outright revolt. My reading of the evidence is that Joseph likely was torn between being deeply committed to Emma while also genuinely believing in the imperative of plural marriage, and thus spent most of the last years of his life trying to convince her that plural marriage could function in the context of their marriage (unsuccessfully). Many accounts suggest that Joseph backed off of the concept multiple times out of deference to Emma (or, rather, that he refrained from placing the doctrine in what he believed to be its rightful place in church doctrine because he feared Emma's reaction).

When Joseph died, there was no clear succession pattern in place, partially because Joseph's only obvious successor was his brother, who was murdered alongside Joseph, and partially because Joseph grew increasingly paranoid towards the end of his life and never was comfortable with potential challengers to his authority lying in wait. Brigham Young, who took control of the largest chunk of the church, was an early adopter of plural marriage, but found himself constantly at odds with Emma Smith, especially over issues of Joseph's legacy (ranging from his private correspondences to key artifacts related to the leadership of the church). When Young led the church to Utah, Emma stayed behind and actually remarried and raised Joseph's children in a mainline protestant environment. Her eldest son, Joseph Smith III, would later play a key role in the founding and leadership of the Reorganized Church of Jesus Christ of Latter Day Saints (RLDS, now renamed the Community of Christ).

This group was made up of folks who had been disaffected from Young's management of the church (as well as Joseph's management late in his life), and had the primary doctrinal belief of rejecting plural marriage. Joseph III maintained throughout his life that it was impossible for his father to have believed in plural marriage, and actually argued that the Utah church's endorsement of the practice was the best evidence that they had perverted the legacy of his father. His primary source on this was likely his mother, who maintained the same position throughout her life (again, probably denialism of some sort, since she almost certainly knew that Joseph at least experimented with the practice). Although the RLDS/CoC never really challenged the Utah church in terms of overall numbers or cultural cache, the rivalry between the two groups was occasionally fierce and violent, and a lot of their differences were articulated by both sides in terms of the relationship to this issue. The Utah church maintained that the RLDS was out of step with Joseph because they denied plural marriage, and the RLDS claimed the plural marriage was evidence of their fallenness and sexual depravity.

One other thing I'll note is that, while there isn't much more than circumstantial evidence for this, I think that the behavior of the disaffected church elites is evidence that Smith was definitely talking about plural marriage even pretty early on. Splinter groups from the church had a tendency to initially denounce plural marriage and then suddenly support it later. Sidney Rigdon is a good example of this tendency, but it happens to several ex-LDS types who had close contact with Smith. The folks who attained that level of closeness with Smith were true believers who uprooted their lives and endured a lot of hardship and danger because they believed that Smith was an organ of God, and even if they initially were revolted by the practice, it would have eaten at them if they were ignoring parts of Smith's teachings, hence the period of rejection followed by periods of acceptance of the practice. But that's just my personal theory.