Here's an answer that says something about what Gandalf used his ring for. It doesn't cite the books though.

One wields it. Then Sauron comes and beats the snot out of one. Then one gets killed.

@Richard That just tells me that the rings helped get them their wealth. It doesn't tell me how the rings managed this. They have the mountains of treasure because of the rings, but how did the rings get that for them?

@Anonymía - If you feel that the present question hasn't attracted the answers you want, the appropriate actions are to a) Post comments asking for additional info. Most users will be happy to oblige or b) Post a bounty explaining that the existing answers have insufficient info.

@Richard Alright then, and I appreciate your help: My uncertainty lies in the fact that the 'true power' of the rings are not known. By true power, I mean the defining attributes they give their bearers, which is described cryptically. For example, The Nine's true powers are not clear, but the bearers of The Nine were described as 'using' the rings to become grand kings and sorcerers, so The Nine clearly had some power besides invisibility if they could attain such stature for their bearers when used (did they give heightened charisma, or mind - control, or 'transported' them into kingship?).

And another thing; Galadriel apparently used her ring to 'create and sustain' Lothlorien. So did the ring 'conjure' up a city, or maybe levitated the stones to build it? Or did simply having the Ring of Water make her so intimidating that people just went ahead and built it for her? Also, Gandalf had the Ring of Fire, and described himself as a servant of the 'secret fire' and welding a 'flame of Anor' when he fought Durin's Bane, so did the ring enhance his Maiar power to the point where hue could slay such a demon?

The question @amaretto linked to seems to be the best target for a duplicate. See this answer.

@randal'thor Again... phrases like '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,' answer nothing that I've asked. Yeah the rings made them kings and wealthy, but how did they do it? Does putting on one of The Nine cause you to become a rich king when you open your eyes? I'm not certain that the answer is that simple.

'They used their rings only for the getting of wealth' does not tell me the means of getting this wealth using the rings. You have the gold, but where did you get it from

'for those who had them in their keeping could ward off the decays of time and postpone the weariness of the world.' So The Three give the immortal and beautiful Elves a resistance to the flow of time? They're already immune to it simply by being Elves. There MUST be something more to their powers.

My fundamental comment would be that it's not clear that the Rings had well-defined powers of the sort you seem to be imagining. I may be able to build that into an answer, but that's the summary of one.

@DeerHunter That tells me that the general power of the rings is longevity, and that Sauron's influence partially shifts non-resiliant mortals into the spirit world. It (again vaguely) mentions enhancing the powers of the user, but to my knowledge, there were not 'powers' for Elves and the mortal races, so I'm not sure what that truly entails. Did Galadriel just have a knack for city-building that her ring amplified?

It mentions that The Seven got the Dwarves their wealth by amplifying bartering skill to the point where they easily got vast wealth through simple trade, which would explain how it 'takes gold to breed gold,' in the sense that the Dwarves had to give something in the 'deals,' or else they weren't using the rings 'dealmaking power'.

The power of the ring overtakes him/her, and he/her wont let anyone near it

@sluger I know that, but that isn't a power granted to the bearers.