The Doctor realized that he's starting to regenerate, as his meeting with the 10th Doctor linked so much more memory that it starts corrupting his mind. He knows that he has 1 more life left after he dies, and is furious, once again, that he is rewarded by none other than dying.
Clara walks into the TARDIS, coming back from taking care of the children she nannys, and sees the Doctor glowing slightly.
"W-what's wrong Doctor? Doctor...? What's that yellow stuff around your hands and head?"
"Clara," he says, holding back his tears, "It's called regeneration. When a Time Lord dies they regenerate their bodies, and have a completely new body, and personality. It's our way of cheating death. The only way I'm as old as I am."
Clara starts to panic, and uses the mental link she still has with River Song to summon her to the TARDIS. River uses her Vortex Manipulator to get to Clara, and is panicked when she sees the Doctor starting to regenerate. Clara, who is two-times more panicked than River, starts asking lots of questions as to what they should do.
"What do we do? Can we help him? Does it hurt him? How many times has this happened to him?..."
The Doctor, overhearing these questions, gets irritated, over-irritated, because of the regeneration process, and starts the actual process. Because of his anger, he wants Clara to shut up, and shoots regeneration energy at Clara, knocking her unconscious. He does the same to River, but that merely knocks her down and out the TARDIS doors, nearly leaving a wound. River gets up and confronts him.
"Stop it, Doctor! You don't know what you're doing!"
He calms down and somehow, stops the process midway, just long enough to say his final words. 'Spoilers.' And continues shooting energy at River, until she's almost dead, and he's done with the process. The new Doctor, almost crying at the sight of River and Clara unconscious, uses all the strength he has to carry them all the way through the long, TARDIS coridoors, to the sick bay, where he runs back to the Library to get a Time Lord Medical book.
LATER
"D-doctor? Hello? Doctor?" Clara asked as she awoke from her deep sleep, caused by the medicine given to her by the Doctor. She sat up, as she saw River trying to open the door with a thin, gold, pen-looking thing, that shone red. As she regained her vision, she could tell it was a device similar to the 'Sonic Screwdriver' the Doctor had.
"This thing?" River asked as she looked back at Clara on the bed, "Sonic Screwdriver, best device in the world, eh?"
"New it..." Clara mumbled under her breath. She stood up fully and walked to the door, next to River. "There isn't even a door handle, how does he even get in and out of the rooms? I've been through the TARDIS, but I've never seen any of the doors closed, they always seemed open." River, ignoring Clara's remark, continued toying with her sonic.
"Ah-ha!" River cheered as her sonic suddenly glowed from the dark-blue-ish purple, to a dark, pulsating red, "I've got a signal on the Doctor, he's in the TARDIS wardrobe." Clara, not knowing how that could help, was amazed as she was suddenly teleported from the medical room to a massive room full of outfits and disguises. She heard a man's voice that wasn't the Doctor's, and was frightened.
"Don't worry dear, it's him. His whole body, personality, and voice changes. It's called re-"
"Yeah, I know, he explained not long before you got here." River, being amazed he had enough time to explain it all to her, proposed they split up and search for the Doctor.
"How will we know where the exit is? The place is bloody massive!" Clara asked.
"Spoilers." River whispered as she ran off into the big curtain, which, as far as Clara could see, was full off Fezes
"Clara!" the Doctor said, as he ran towards Clara from the hallways that led to the room. He grabbed her shoulders as he asked "Where is River?"
"She just went into there,why?" She replied, as the newly regenerated Doctor took off into the curtain.
As Clara heard an explosion, she saw the Doctor and River both dash out of the curtain, panicked, yelling "RUN!" and grabbing Clara's arms, rushing her along back to the console room, and out of the TARDIS. The Doctor closed and locked the TARDIS doors, and grabbed each of the girl's arms' and ran into Clara's house. He covered their ears, as the TARDIS exploded, not very far from the house. He uncovered their ears, and looked out the window. All he saw was a crater, and the blue-box in the bottom of it, with both doors blown off, and the TARDIS was empty. The TARDIS had died forever. It wouldn't regenerate. It wouldn't come back by some miracle. It was gone for good. And it would never come back, for as long as the Doctor lived.