How did David do this?

I don't really see how would David put Shaw together after ripping her jaw like that drawing depicts. For all, we know he used her organs for his experiments.

It could just be some illustration drawn by David for some reason that has nothing to do with actual Shaw's corpse. There was another drawing of Shaw drawn by David when Daniels was turning over those sheets of paper.

And there are other drawings depicting Shaw that we didn't actually see in the movie like these

I agree with Dark Nebula. 

Some of the drawings seem to be projected mutation of Dr. Shaw based on David 8's studies. David 8 has mentioned "reanimation" in describing his work, so who know's what that means.

Yes, it was suggested that some drawings show David's dreams/nightmares.

Android dreams.

Android fantasies more like. David was twisted.

I hope David gets his for what he did to Shaw. I feel badly for Daniels but David killing Shaw is just unforgivable. I remember watching Covenant for the first time in theaters and being so pissed at the end after seeing Shaw vivisected in David's lab. Even if she were to die from an infection from her surgery wound I'd be much more accepting of that than having David presumably strangling her and then experimenting with her insides. I know David "loved" Shaw but at this point I hope if he makes Daniels into a queen that she sticks her tail through his torso and rips him in half a la Bishop in Aliens. >:/

David is a great antagonist, showcased far more than some appreciate, and should be reconciled with his works JakeBranson in some great fashion...torn apart, dropped in lava or into a star.  David was bisected by an Engineer and still managed to wipe out all Engineer social activity on Planet 4 shortly after.  So, yes, "he" will get his.  I hope.

I do expect David to live on as a "Personality" in Mother if that happens due to the below explanation on page 35 of The Weyland-Yutani Report.  Ash did in a novel and interacted with Ripley before the events shown in Aliens.

"'Personality' subprograms could be downloaded depending on the AP application, and all models ran a laboratory installed subprogram that ensured complete loyalty to Company interests."

Missed this Topic but covered similar.

What we have is as Dark Nebula mentioned, that Hatton and Hallet had produced a Number of Drawings with Dr Shaw, and it was deemed to be COOL to add their work into the Movie for just a Brief Glimpse.

The Artist had Discussed these in the Past and gave some Alternative/Ambiguous reasons for them. They Suggested/Pondered that maybe David had Cloned her? or he had Resurrected/Repaired her?

But they also said or they could be the Twisted Dreams/Vision that he had that he chose to Draw, and i think this is the LIKELY explanation if we are looking at the most Suited/Logical Explanation.

We have to Wonder would he actually try and Carry some of these Dreams/Visions out on Daniels ;)

I think to look at what JakeBranson had put then i think yes it was a Shame they Killed off Dr Shaw with NO real role for her to Play, but there are STUDIO reasons for this. But Noomi Rapace did have some Free-Time in her Schedule to Shoot the Crossing, and she could have had a Free Period to give her a Small Role in the Movie... she was disappointed at NOT being involved as she felt her Characters Story had more to be TOLD.

Katherine Waterston did comment that she heard there was some Interesting Things as far as her Character, but she then added that she could just as likely END-UP in a Body Bag...  which is to show she is AWARE that there is No Guarantee they would use her, and she could become a Experimented on Afterthought like Dr Shaw was.

There is some Mystery and Untold Events from the Moment until Dr Shaw took her LAST Breath and the Moment she had been Tucked into Cryo-Sleep in The Crossing.

There is a Story there that would be ok for a Novel, a Very Sad and Disturbing Story that would Delve into the Mind of David and his Actions/Thinking.