For those without DDI subscriptions:
You choose two classes. Each class has a unique entry - "Hybrid Cleric" for example. I'll use clerics and fighters as examples, but they give us all the PHB1 classes as well as the swordmage in the preview.
Each entry lists the armor, weapons, and implements you become proficient in (although you only gain proficiency in armor shared by both classes), and the bonuses you gain to defenses. You combine the defense bonuses: cleric gets +1 Will, fighter gets +1 Fortitude, etc.
You also gain a combination of hit points at 1st level and every level after. Hyrbid clerics get 6 hp at 1st level and 2 at every level gained. Fighters gain 7 and 3. The same goes for healing surges - clerics get 3 surges per day, fighters 4.
You combine the list of class skills from both classes and gain 3 trained skills from that list. Some classes grant you extra trained skills - rangers get 1, rogues get 2, for example.
When you select your powers, you get 1 at-will from each hybrid class. When you get 2 or more powers in a category at least 1 of those powers must come from each class.
You gain the class features listed for your hybrid classes, which are watered down when compared to the true class. Hybrid clerics get Healer's Lore and Healing Word, though they can only use the later 1/encounter. Fighters only gain Combat Challenge and can only mark enemies with fighter powers/fighter paragon path powers.
You are considered a member of both classes for meeting pre-reqs, for things such as feats and paragon paths. Your class features still count as the original version for meeting pre-reqs too.
You can still take multiclass feats!
That's it, mostly.