This is just a unified “how it works” section for all the psionic classes, so I’m not reposting the same thing for every psionic class. That’s Ardent, Divine Mind, Erudite, Lurk, Psion, Psychic Rogue, Psychic Warrior, and Wilder.
As D&D’s redheaded stepchild, there’s not a great deal of psionic material. There are only two dedicated psionic books in the 3.5 library; Expanded Psionics Handbook and Complete Psionic, which is generally regarded as the worst of the Complete series (though it is still decent for extra content). Also, there’s the Mind’s Eye, which is a series of WotC web enhancements that amounts to a third psionic sourcebook. Other than that, bits and pieces of psionic material have cropped up randomly throughout the library whenever WotC remembered they exist and probably needed to pad a book a bit. Sandstorm and Races of Stone have psionic material. Eberron has significant psionic material as well.
So, first, what is psionics? Quite simply, it’s a magic system designed specifically for spontaneous casting. Nothing more, nothing less. Some people decry psionics for the very word, yet overall, it’s far truer to most classical depictions of magi in fantasy than Vancian. In fact, other than in Vance’s own works, Vancian is fairly rare, and it’s fairly silly to boot.
Psionics are not science fiction. This is a myth, and it is baseless. If you don’t like the words “psionic” or “manifest,” that’s fine, but they need ever come up in-character. When describing my psionic characters in-character, they’re not “psions who manifest powers,” they’re “mages who cast spells.” That’s not refluffing. That’s what they are. The effects are magic, and unless you want to houserule it, “Psionics are magic,” is an explicitly stated rule. The variant, “Psionics is different,” is basically prefaced with, “This is a bad idea.”
I know this has little to do with how psionics work, but it’s a necessary preface to any discussion of psionics as a whole, so it goes here in the primer. There are far too many people who write psionics off with, “Bester has no place in D&D,” without ever actually looking at the material (or worse, just looking at the pictures of creepy bald dudes with crystal fetishes). Hell, I used to hold that position, and it was blatant idiocy on my part. (And the standard disclaimer: This does not mean anyone who doesn’t have psionics in their games is Doing It Wrong.)
Of equal importance, 3.5 psionics are not 1e psionics. 3.5 psionics aren’t 2e psionics. 3.5 psionics aren’t even 3e psionics. Yes, in the older editions, psionics were totally broken. 3.5 is not the older editions, and 3.5 psionics are not the older editions’ psionics. In another case of “all too often,” people accuse psionics of being broken based on older editions. Or based on someone in their group who ignored a lot of the rules that balance it. Or call it “too complicated” when psionics are vastly simpler than Vancian, and they’re just less familiar with psionics, which is a completely separate issue, and one that’s completely temporary.
Anyways, on to the actual mechanics. First, the vocabulary. “Manifest” is another word for “cast.” “Power” is another word for “spells. “Power points” are the currency that replaces spell slots. “Disciplines” replace “schools” for magic spell, and psionics have their own divisions.
With Vancian, you generally keep track of up to ten pools of points- the spell slots from cantrips to 9th level spells- and every spell costs one point. With psionics, you have only one pool of points, your power points, but powers have a variable cost. Each level of powers has a minimum cost (1 for 1st-level, 3 for 2nd, 5 for 3rd, and so on through 17 for 9th). Thus, five power points are roughly comparable to a third level spell slot. You get so many points per level, and there is a table for determining bonus power points from high ability scores, much like with magic. You can spend your points to cast any of your limited powers known, so long as you have the points.
Manifesting a power works mostly like casting a spell, however powers do not have verbal components, nor do they have somatic components, nor are they subject to arcane spell failure, so psionic characters can legally use armor with little penalty and they’re capable of manifesting powers in a number of situations where magic-users can’t. Like when polymorphed into a housecat. Oddly, the circumstances that force Concentration checks are the same, so you need to make a Concentration check to manifest while entangled, but you can manifest without penalty when completely paralyzed.
For the most part, other than effects like range and duration, powers do not scale naturally. A Psion spending one point to manifest Energy Ray (which is, unsurprisingly, a ray attack that deals energy damage) can only deal one die of damage, whether they’re 1st-level or 20th. What psionics does have, however, is an augmentation system. A one-point Energy Ray deals one point of damage, but a two-point Energy Ray deals two die of damage and a twenty-point Energy Ray deals twenty die of damage. Depending on the power, there can be various augmentations like increased saves, affecting additional creature types, increased duration, and so on. This lets powers age much better than spells, and stay useful for much longer. Even though you’ll have fewer powers than, say, a Sorcerer, it’s not a huge deal since your powers stay useful longer.
This does not mean that a 10th-level Psion with a hundred power points can blow them all on a hundred-die Energy Ray. One of the most important rules in psionics is that you cannot spend more points on a power than your manifester level (translation: caster level), save through a scant few abilities that let you reach a little higher than normal. So no blowing a hundred points on a power unless you’re level 100.
Also, XPH introduces psionic focus. In short? Make a Concentration check as a full-round action. If it’s 20+, you’re focused. It doesn’t really do much on its own, though you can expend focus to take 15 on a single Concentration check (making you not-focused). Mostly, it’s another form of currency that numerous other abilities rely on. Some bonuses are only available while focused, some abilities require you to expend focus. For example, metapsionic feats increase the power point cost of a power (still subject to standard limits) and require you to expend psionic focus, so don’t expect to ever pile on three or four metapsionic feats on the same power, even if you can spend the points.
And that covers the bulk of it. The rest are the details of the powers, classes, and feats themselves.
On the whole, psionics is more streamlined and intuitive than Vancian (and more balanced, to boot), and the way the powers and augmentations work, powers are far more a part of the character that can stick with you from beginning to end than something you just use for a little while only to toss it out for something completely different a couple levels later.