The short version is by hand. Wallace drafted his fiction and essays in longhand before anything went near a keyboard, and he revised each page far more than most readers would guess.

The Direct Answer
He wrote first drafts in longhand, revised obsessively, then typed.
The handwritten drafts, later transcribed, are documented in his archive at the Harry Ransom Center.

Longhand, in Pencil and Pen

Wallace worked the same way for years. He filled spiral notebooks by hand, in pencil and pen, then transcribed the pages onto a computer once a passage held its shape. He said the slowness was the point. Typing was faster, and speed was exactly what he didn't want when he was trying to think. The first two or three drafts, by his own account, were always longhand.

Revision was where most of the work happened. His typescripts at the University of Texas carry corrections in different colored inks, one color per pass, so you can watch him go back over the same page again and again. He wrote much of Infinite Jest this way in the early-to-mid 1990s, starting the novel in 1991 and handing a draft to his editor by the end of 1993.

The Footnotes Were a Choice

The endnotes in Infinite Jest and the footnotes in his essays weren't decoration. Wallace used them on purpose, to break a linear text into something closer to how he felt modern life actually arrives, in fragments and interruptions. He explained the thinking to Charlie Rose in 1997.

There's a way that it seems to me reality's fractured right now, at least the reality that I live in.

David Foster Wallace, Charlie Rose interview, 1997

Read the full David Foster Wallace writing routine for how the drafting and revising fit with his teaching years.

What You Can Steal