Sauron was among the mightiest of the Maiar. Originally of Aulë's people, he acquired great "scientific" knowledge of the world's substances and how to use them. He would retain this knowledge throughout his tenure as the Dark Lord in Middle-earth, using it to forge the One Ring and construct his fortress of Barad-dûr. Sauron also seemed primarily linked to the use of fire, and as Morgoth's chief lieutenant, his ability to tap into the fires in the earth was of great value.
Among Sauron's chief powers were deception and disguise: In the First Age Sauron took on many forms. His battle against Luthien and Huan in The Silmarillion has him taking on no less than four separate shapes: his "normal" shape, presumed to be that of some kind of terrible dark sorcerer, a great wolf, a serpent, and finally a vampire "dripping blood from his throat upon the trees" ("Of Beren and Lúthien," The Silmarillion). At the end of the First Age, Sauron took on a fair form to appeal to the Captain of the Hosts of the Valar and ask for pardon. In the Second Age, Sauron took up that fair form again and used it under the alias "Annatar" to deceive the Elves into creating the Rings of Power. The level of deception required to fool the Elves of Eregion must have gone beyond simply taking on a fair form. Sauron was literally instructing the Elves to make artifacts that while capable of great good, were ultimately purposed for his own domination and were imbued with power to arrest the natural order of the world. The Elves were unaware of who they were dealing with until the eleventh hour, and only narrowly escaped his trap. Centuries later, Sauron was able to deceive the Númenóreans and steer them directly to their own destruction under promises of eternal life. Such destruction is a testament to Sauron's manipulative nature and ability to twist the perceptions of his enemies.
An interesting dichotomy is set up between his deceptive nature and his symbol. While rarely appearing personally and deceiving all but the most wary, he represented himself as an all seeing eye that could pierce all disguises. Consistent with Tolkien's theme of evil being finite, wasteful, and self-destructive, Sauron's powers gradually decreased as time went on. After the Fall of Númenor he was incapable of taking physical form for many years, and then later became a horrific Dark Lord. After losing the Ring it took even longer for him to regain physical form, although by the War of the Ring he had regained it.
The extent, nature, and specifics of Sauron's power are largely left to the imagination. Like his master Morgoth, he was capable of altering the physical substance of the world around him by mere effort of will.