Two part question: Why did the races accept the rings and what did they expect from them. Also, did they corrupt the same way the One Ring corrupts? Just wasn't sure about why they took them, if they knew they were from Sauron , and what exactly was the corruption they caused.
This is all answered in "Of the Rings of Power and the Third Age" in the published Silmarillion, but in summary, DVK's comment is correct: they weren't aware that Sauron was bad - at least at first.
Regarding the making of the Rings, this was done by the Elven smiths of Eregion (which the Fellowship pass through the ruins of on their way to Moria) early in the Second Age, when Sauron came among them, put on his beautiful form, and took the name Annatar: Lord of Gifts.
But wherefore should Middle-earth remain for ever desolate and dark, whereas the Elves could make it as fair as Eressea, nay even as Valinor? And since you have not returned thither, as you might, I perceive that you love this Middle-earth, as do I. Is it not then our task to labour together for its enrichment, and for the raising of all the Elven-kindreds that wander here untaught to the height of that power and knowledge which those have who are beyond the Sea?
Cunning words, because this was exactly what the Elves wanted - to have their own kingdoms in Middle-earth that they could rule according to their own desires, but also to forestall the passage of time and preserve much of what was fading.
That supplies the answer for the Elves, but they didn't accept Rings from Sauron; they were instead the people who had originally made them - all of them, aside from the One.
As soon as Sauron made the One and wore it for the first time, the Elves were aware of what he was up to, and took off their own Rings.
The Three Elven Rings were marked as special, as different from the others:
the Three that had last been made, and they possessed the greatest powers ... those who had them in their keeping could ward off the decays of time and postpone the weariness of the world ... they were forged by Celebrimbor alone, and the hand of Sauron had never touched them; yet they also were subject to the One.
Following this incident, the Elves and Sauron fought a number of wars during which Sauron laid waste to Eregion and collected the other Rings, which he then gave to Men and Dwarves.
Dwarves indeed proved tough and hard to tame; they ill endure the domination of others, and the thoughts of their hearts are hard to fathom, nor can they be turned to shadows. They used their rings only for the getting of wealth; but wrath and an over-mastering greed of gold were kindled in their hearts, of which evil enough after came to the profit of Sauron.
Men proved easier to ensnare. Those who used the Nine Rings became mighty in their day, kings, sorcerers, and warriors of old. They obtained glory and great wealth, yet it turned to their undoing. They had, as it seemed, unending life, yet life became unendurable to them. They could walk, if they would, unseen by all eyes in this world beneath the sun, and they could see things in worlds invisible to mortal men...
Tolkien doesn't clearly state how Sauron was able to convince Men and Dwarves to take the Rings in the first place, but one can easily imagine that he used a similar tactic as his initial one with the Elves.