The Rune Scribe is the first of the new Prestige classes planned for Dungeons & Dragons 5th Edition. As the name implies, it also brings with it the first experimental rules for including Rune Magic in 5e. It can be found in the October 2015 Unearthed Arcana article on the WotC website - or just take it from here: http://media.wizards.com/2015/downloads/dnd/UA_Rune_Magic_Prestige_Class.pdf
To enter the Rune Scribe class, you need a character to be at least 5th level. It also requires a minimum of 13 in both Dexterity and Intelligence. It's also got a special requirement: you need to find a rune and present it to an NPC Rune Scribe in order to receive tutelage, and since you're being tutored, you can't get to any Rune Scribe level that your tutor doesn't have. So, if all you find is a level 2 Rune Scribe to teach you, to take a 3rd level in this PrC, you gotta go and find a new tutor and impress them over again.
The Rune Scribe is a 5 level PrC with the following goodies to be had from taking it.
Firstly, you run off of a D8 hit dice, meaning you get 1D8+Con Modifier new hit dice each level of Rune Scribe you take. This could be quite handy for squishier characters, like the Wizard, Sorcerer, Warlock or Arcane Trickster Rogue, and means it doesn't shortchange beefier opt-ins, like an Eldritch Knight Fighter.
Secondly, you get free proficiency with Calligraphy, Masonry and Woodcarving tools.
You gain two 1st level spell slots at 1st level, increasing to three at level 2 and four at level 3. You also get two 2nd level spell slots at 3rd level (increasing to four at level 4) and two 3rd level spell slots at 5th level.
As for unique class attributes, you get the following:
Rune Lore: This ability, gained at 1st level, lets a Rune Scribe unlock the Complex Properties of Master Runes.
Runic Magic: A Rune Scribe does not learn any spells when it gains spell-slots, as it gains said spell-slots for the sake of empowering Master Runes. As per the 5e rules for Multiclassing, Rune Scribe spell-slots stack with spell-slots gained from other spellcasting classes, so a Wizard 6/Rune Scribe 4 has spell-slots as per a 10th level character. This ability is gained at 1st level.
Runic Discovery: At 2nd, 3rd and 5th levels, a Rune Scribe becomes able to attune themselves to one Rune without having the Master Rune for it. It requires a short rest to attune or unattune from a chosen Rune.
Living Rune: From 4th level on, a Rune Scribe can freely boost either one ability score by +2 or two ability scores by +1 at the end of a long rest. This boost lasts until they next take a long rest, which means they can only have 1 (or 2) modified stats at any one time.
Rune Mastery: A 5th level Rune Scribe may choose for one attuned Rune to not count towards their maximum number of attuned magical items. To change the "extra" rune, a Rune Scribe has to unattune from it first.
Wait, Rune Magic?
A new sub-system of magic included to go with the Rune Scribe. In essence, Runes are treated as magical items - Master Runes are fully-enchanted copies of a rune inscribed on some substance or other, allowing anybody to pick it up and attune to it. Once attuned, a Rune provides access to a number of powers, which are divided between Simple Properties (anyone can use these) and Complex Properties (you need the Rune Lore class feature to use them). Master Runes, like any other magical item, can only be attuned to one person at a time, so not just anyone can use them.
Only four Runes have been created so far. They're repeated below, because we're nice like that.
Ild: The Rune of Fire gives you skills relating to burninating shit. It has the Simple Properties of Ignite (immediately set fire to any flammable object), Fire Tamer (can extinguish any fire within 10ft, or boost it by expending spell-slots; +20 feet of extinguishing per spell level expended) and Fire's Friend (resistance to Cold). Its Complex Properties are Combustion (touch a critter and expend a spell slot to do 1D10 + 1D10/spell slot level Fire damage), Flame Brand (enchant a weapon or ammunition to do fire damage instead of physical for 24 hours), and Flame Stoker (when dealing Fire damage, roll the damage dice twice and use the higher result).
Stein: The Rune of Stone gives you skills relating to the strength of the earth. It has the Simple Properties of Indomitable Stand (create a rune on the ground that stops creatures getting within 10 feet of you and gives you Advantage on resisting attempts to be moved), Stone Soul (you can't be petrified) and Stone's Secrets (touch a stone/earth floor or wall to learn the location & size of anything touching that surface within 30 feet). Its Complex Properties are Crushing Brand (imbue a bludgeoning damage weapon with the ability to ignore bludgeoning resistance/immunity for 24 hours), Earthen Step (Meld Into Stone 1/short rest) and Overwhelming Bolt (touch a creature and expend a spell slot; they must pass a Strength check of 12 + expended spell level or take 2D8 + 1d8/spell level bludgeoning damage and be knocked prone; success halves damage and negates the knocked prone effect).
Vind: The Rune of Air gives you skills relating to mastery of air. It has the Simple Properties of Comforting Wind (cannot suffocate, cannot drown, Advantage on saving throws vs poisonous gas, inhaled poison, etc), Wind Step (fly 20 feet as an action) and Wind's Grasp (spend a reaction whilst falling to take no falling damage). Its Complex Properties are Howling Brand (enchant a ranged weapon to double its range and ignore range disadvantage for 24 hours), Shrieking Bolt (blast a target within sight, forcing a Strength check of 12 + expended spell level or take 2D8 + 1d8/spell level bludgeoning damage and be pushed 10 feet per expended spell level; success halves damage and negates the push effect) and Wind Walker (Levitate 1/short rest).
Kalt: The Rune of Frost gives you skills relating to freezing shit. It has the Simple Properties of Frigid Touch (freeze 10ft radius of water by touching it), Frost Friend (resistance to Fire) and Icy Mantle (create a mantle of ice that absorbs all damage from the next bludgeoning/slashing/piercing attack, then shatters). Its Complex Properties are Freezing Bolt (touch a target whilst expending a spell slot and force them to take a Constitution check of 12 + expended spell level or take 2D8 + 1d8/spell level Cold damage and have speed reduced to 0 until end of next turn; success halves damage and negates the slow effect), Ice Brand (enchant a weapon or ammunition to do Cold damage instead of physical for 24 hours) and Winter's Howl (Sleet Storm 1/short rest).