Sauron seems to be able to build armies and enslave races just fine without his ring. Are there any mentions in the Lord of the Rings movies or books as to what the powers of the ring actually are?
There is a nice summary of that on Wikipedia:
The Ring's primary power was control of the other Rings of Power and domination of the wills of their users. The Ring also conferred power to dominate the wills of other beings whether they were wearing Rings or not — but only in proportion to the user's native capacity. In the same way, it amplified any inherent power its owner possessed.
A mortal wearing the Ring became effectively invisible except to those able to perceive the non-physical world, with only a thin, shaky shadow discernible in the brightest sunlight. The Ring would also extend the life of a mortal possessor indefinitely by preventing natural aging. Gandalf explained that it does not "grant new life", but that the possessor merely "continues" until life becomes unbearably wearisome. However, the Ring could not protect its bearer from destruction; Gollum perished in the Crack of Doom while in possession of the Ring, and even Sauron himself could not preserve his body from destruction during the downfall of Númenor. Likewise, the Ring could not protect its bearer from physical harm; Frodo was seriously injured by the Witch-king on Weathertop, and lost a finger when Gollum bit it off — on both occasions while wearing the Ring. Sauron himself suffered the death of his physical body at the hands of Gil-galad and Elendil while wearing the Ring. Like the Nine Rings, the One Ring could physically corrupt mortals who wear it for extended periods of time, eventually transforming them into wraiths. Hobbits were resistant to this process: Gollum had not become wraith-like despite his possession over several centuries.
The Ring might also have given its wielder the ability to read minds, as Galadriel suggested to Frodo when he wondered why he could not read the thoughts of others as she did.
Within the land of Mordor where it was forged, the Ring's power increased so significantly that even without wearing it the bearer could draw upon it, and could acquire an aura of terrible power. When Sam encountered an orc in the Tower of Cirith Ungol while holding the Ring, he appeared to the orc as a powerful warrior cloaked in shadow "[holding] some nameless menace of power and doom." The orc was so terrified that it fled. Similarly at Mount Doom, when Frodo and Sam were attacked by Gollum, Frodo grabbed the Ring and appeared as "a figure robed in white... [that] held a wheel of fire." Frodo told Gollum "in a commanding voice" that "If you touch me ever again, you shall be cast yourself into the Fire of Doom," a statement fulfilled when Gollum fell into Mount Doom with the Ring. Although the Ring was certainly invoked with this statement, it is unclear whether Frodo was prophesying (Frodo had previously seen less sinister visions while in possession of the Ring), or if Frodo was actively laying a curse upon Gollum.
As the Ring contained a large part of Sauron's power, it was endowed with a malevolent sentience of sorts. While separated from Sauron, the Ring would strive to return to him by manipulating its bearer to claim ownership of it, or by abandoning the bearer at an opportune moment. For example, it slipped from Isildur's finger during the ambush at Gladden Fields; moments later he was killed by orcs, leaving the Ring's whereabouts unknown to Sauron's enemies. It also slipped off Gollum's finger when the time was right for it to be brought back into the world at large. Warned by Bilbo of the Ring's tendency to slip off, Frodo carried the Ring on a chain.
To master all of the Ring's capabilities, a Ring wielder would need a disciplined and well-trained mind, a strong will, and great native power. Those with weaker minds, such as Hobbits and lesser Men, would gain little benefit from the Ring, let alone realize its full potential. Even for someone with the necessary strength it would have taken time to master the Ring's power to the point where he was strong enough to overthrow Sauron. Ironically, the prospect of mastery is the main appeal that the Ring holds for those who come in contact with it. The Ring appears as a symbol of hope, offering the power to defeat Sauron and bring peace to the world. Yet in the end, its inherent malevolence would twist its bearer into another Dark Lord as evil as Sauron, regardless of one's intentions at the outset.
Despite its power, the Ring did not render its bearer omnipotent. Three times Sauron suffered military defeat while bearing the Ring, first by Gil-galad in the War of Sauron and the Elves, again by Ar-Pharazôn when Númenórean power so overawed his armies that they deserted him, and again at the end of the Second Age with his personal defeat by Gil-galad and Elendil. Tolkien indicates, however, that such a defeat would not have been possible in the waning years of the Third Age, when the strength of the free peoples was greatly diminished. There were no remaining heroes of the stature of Gil-galad, Elendil, or Isildur; the strength of the Elves was fading and they were departing to the Blessed Realm; the Dwarves had been driven out of Moria and would have been unwilling to concentrate their strength in any event; and the Númenórean kingdoms had either declined or been destroyed, and had few allies.
Sauron had no trouble creating an Orc army and enlisting various corrupt beings (mercenaries and such), but enslaving other races to his will is a different thing. He wouldn't be so fiercely opposed by all the Men and some of the Elves if he could've just enslaved them.