The most recent Unearthed Arcana article on the official Dungeons & Dragons website has added playtest material for psionic characters, some of which appeared in different forms in older editions of the game.
Psionics have always been a touchy subject with Dungeons & Dragons players, as the rules behind them haven't always been solid. The new psionic classes for the fifth edition of Dungeons & Dragons are also a mixed bag and a DM should be wary of using them without being aware of the kinds of things they can do with their powers.
The Psychic Warrior Archetype For Fighters
Psychic warrior is an archetype for fighters that they can take at third level, which means that they have to run around as standard warriors before their x-gene develops and they gain mutant powers.
The psychic warrior gains some incredible buffing abilities, as Augmented Defenses allows them to spend their reaction to take 1d10 away from the damage dealt to a party member. Telekinetic Bulwark grants half-cover in a ten-feet direction and grants advantage on Strength checks, while also lasting for a minute and not requiring concentration. The Strength of Mind ability is also good, as it's a psychic whip that can be used as a bonus action each round to either push or pull an opponent.
The best build for a psychic warrior is a defense-focused character with a high Intelligence score, as almost all of their abilities are tied to their Intelligence modifier. Think of them in a similar manner to the warlord from the fourth edition, as they can use their powers to protect their allies and move enemies around the battlefield, while still being able to dish out damage.
The Soulknife Archetype For Rogues
Soulknife is a rogue archetype that they can choose at third level. Their main ability is Psychic Blade, which allows them to manifest a weapon out of psionic energy at any time and even throw it at their enemy, though it disappears shortly after. The ability to always be armed shouldn't be understated and it would be incredibly useful in situations when the party is captured.
A soulknife gains access to the Psionic Enchantment ability at level three, which lets them choose one of three powers that they can switch on their next long rest. The best of these is the one that grants them telepathy (unless they have the Telepathic feat listed below), as completely silent communication is an incredible tool for a rogue to have.
The powers of a soulknife become less impressive over time, as Terrifying Blade only causes the frightened status for one turn, while Psychic Veil allows the soulknife to become invisible for ten minutes, which isn't that impressive for a thirteenth-level ability. These weaknesses aside, a telepathic assassin who can never be disarmed is a frightening prospect and would be especially useful in an adventure set in a civilized area, where enemies can be reasons with (or blackmailed) and imprisonment is a real possibility.
The Psionics Arcane Tradition For Wizards
A wizard can choose the psionics Arcane Tradition at second level, which allows them to improve some of their cantrips using their new psionic focus. The real benefit of choosing psionics is the Thought Form ability at level six, which is one of the most broken abilities in the Unearthed Arcana article.
Thought Form is the Super Saiyan transformation of the wizard class, as it lasts for ten minutes without concentration, lets them cast all spells without any verbal/somatic/material components (outside of those that cost more than a gold piece), and gives them resistance against psychic damage and nonmagical attacks. Thought Form is an unbelievably powerful ability and probably shouldn't be allowed by most DMs.
A psionics wizard is essentially a far superior version of the enchanter. Thought Form is way better than Hypnotic Gaze and most players would be better off choosing psionics as a result.
Psionic Feats & Spells
There are two psionic feats available and one is definitely better than the other. The Telekinetic feat is decent, as it allows the player to potentially push an opponent back a step using their bonus action, but Telepathic Feat is the superior of the two, as it allows a character to mentally communicate with another person within thirty feet. Having permanent access to telepathy can allow players to prepare actions while around potential opponents without giving any indication that they are plotting something, which can be abused in a number of ways.
The psionic spells are a mixed bag. Ego Whip is a powerful debuff spell, but it has a short-range, requires concentration, and the enemy can save each turn. Id Insinuation deals 1d12 psychic damage to an opponent each turn and has a decent range, but it also requires concentration and has a saving throw. Intellect Fortress gives the player an advantage on saving throws and lets them use their reaction to let allies within thirty feet reroll a failed save. Mental Barrier is interesting because it's a reaction spell that gives advantage on Intelligence, Wisdom, and Charisma saves, while also granting resistance to psychic damage, but it only lasts until the start of the next turn.
Mind Silver is a decent cantrip, as it deals 1d6 psychic damage on a failed Intelligence save and subtracts 1d4 from the enemy's next saving throw. Mind Thrust might be the best psionic spell, as it's a second level spell that only requires a bonus action to cast, has a sixty-foot range, deals 3d6 damage on a failed intelligence save, and the enemy can only Dash or Disengage on their next turn. Better yet, it can be improved by spending a higher-level spell slot in order to make it target multiple opponents.
Psionic Blast is like a stronger version of Thunderwave, as it fires a thirty-foot cone of energy that deals 5d8 damage and pushes the enemy back by twenty-feet if they fail a Dexterity save. Psychic Crush can deal 12d6 damage and stun an enemy for one minute if they fail an Intelligence save, but the enemy gets a new save at the end of each turn to break out of the stun. Thought Shield can protect an individual's mind from being read for eight hours without needing to concentrate, but this would only be useful under very specific circumstances.
Source: Dungeons & Dragons