From the comics:
In 2015, the Marvel Multiverse was destroyed and (for the most part) recreated due to the events of the Secret Wars storyline. In the old universe, the stones (then called the Infinity Gems) had the powers described in the following image (located in Marbvel Fact Files #001 by Valorum
- Soul: Per the image, allowed the user to manipulate the souls of the living and the dead. The Soul Stone was used by Adam Warlock for many years, and was the gem we saw working more often than all the others combined. It seemed to have the ability to either drain parts of people's souls into itself, or to copy those souls in some fashion. Originally, this seemed like an almost vampiric ability; one that Adam generally avoided using except on people who were already dying. Due to this, parts (or copies) of the souls of his friends, Gamora and Pip the Troll, and of Adam himself (due to timey-wimey shenanigans) wound up in the stone. The stone was therefore instrumental in the return of those three to life years later (around the time Thanos actually first assembled the stones into the Infinity Gauntlet). And, in the comics, the piece/copy of her soul is currently driving Gamora - she feels as if she is incomplete somehow.
- Mind: Grants power over minds and dreams to the wielder. Not seen to be used independently.
- Space: Grants the ability to exist in any and all locations as well as to warp space (i.e., teleport).
- Time: "Total control of the past, present, and future." In practice, this seemed to grant the wielder the ability to more through time at will, and to speed up or slow down time for others (presumably using to grow gardens quickly).
- Power: Grants access to "any and all energy that has or ever will exist"; in practice, as the two guys we saw wielding it alone were Drax and the Cahmpion, both of whose primary powers at the time were physical strength, it made them stronger. Also, boosts the powers of the other gems (which, from the descriptions here, had such vast limitations).
- Reality: "Allows the user to fulfill any desire, even if it contradicts physical laws." In practice, I don't think we knowingly saw anyone use this gem independent of the others.
It was established that the stones only worked in their native realities, in the Avengers/JLA crossover in the early 2000s; we saw Darkseid trying to use the Infinity Gauntlet in the DC universe, but there it's just a gaudy glove.
Since the new version of the uni/multiverse returned, the Gems are now the Infinity Stones (All but the souls stone have a rough, uncut/unpolished appearance). The colors associated with the various stones have changed (for example, the Soul stone was green previously, and is orange now). And, it appears how they work has been redefined. I'm going to assume that these changes were to better match the movies.
Here's a page that explains how the stones now work in the comics, from INFINITY COUNTDOWN #1:
Here's a blow-up of the details on the new reality stone:
And, yes, different people can use the stones at different levels. In the comics, we've seen this in practice. The Space stone has been held by both Wolverine and Black Widow. Wolverine was ability to use the stone to teleport much farther than the Widow - she was basically limited to line-of-sight jumps. this implies that Wolverine has a greater "mastery" of power (physical power) than the Widow. He's stronger than she is, and ha the whole regeneration thing going on, which may explain the difference.
The description of the Mind stone says it can grant "telepathy or intelligence." For the holder in the Infinity Countdown series, it definitely seems to have granted both. It may raise intelligence to a degree, but have a point where it levels off. If Tony Stark or Bruce Banner had the stone, it might not boost their intelligence much at all.
So, "mastery" of one stone's realm controls how much you can do with that stone. If you happened to have the Time stone and the Reality stone, your access to the Time stone would give you better mastery of Time, and thus power up your ability to use the Reality stone.
As stated at the bottom of that page:
On their own, the stones provide great power. But when combined, they form a circuit -- a positive feedback loop granting the user INFINITE power!
Again, there's no guarantee that this is how the stones work in the movies. However, it seems unlikely that Marvel would go to lengths to explain how they work together for the first time ever, and explicitly not try to match things up with the MCU.
For the most part, the powers are as described above. The main differences:
- No mention has been made of the quasi-vampiric aspect of the Soul stone. Otherwise, it seems unchanged;
- If the Space stone used to grant the wielder the ability to stay alive in hostile location (not clear from the description), no mention is made of that now;
- the Power stone makes you more physically powerful, explicitly (from the description of the old gem, I would expect it to make, say, Professor X a more powerful telepath); and
- the Reality stone now is defined as granting the ability to access the multiverse.