Two Player Draft Formats
The two player formats I know of are:

Solomon draft
Winston draft
Winchester draft

Wizards has some information about these 'casual' formats.
Common Setup
Each of these draft formats uses a similar setup:
3 packs per player (6 total)
Open all the packs, without looking at them, and remove any basic lands then shuffle all the cards together. You should have between 84 and 90 cards depending on the sets the boosters came from (14+basic or 15 cards in each).
Instead of using new boosters one can build a draft pool by:

Shuffle up an existing sealed deck pool.
Shuffle two sealed pools (12 packs total) together and draw off 90 cards.
Shuffle a Cube and draw off 90 cards.

Decide on a minimum deck size (30 or 40, see below.)
Randomly decide who drafts first.
Solomon Draft
Players alternate drawing 8 cards and separating them into two piles, then the opposing player chooses a pile and the separating player keeps the other.
The piles need not be even.
When there are less than 8 cards left in the draft deck/pool the draft is over, the remaining cards are not used.
Winston draft
Begin by dealing out 3 face down cards, these become the draft piles.
Players alternate looking through each pile in turn, they may either take the pile or look at the next. If no pile is chosen the player drafts the top card of the draft deck. Then deals a face down card to each pile the player passed on, plus one card to replace the pile they took. The draft ends when all the cards are drafted.
The piles have no maximum size.
Winchester draft
Begin by dealing out 4 face up cards, these become the draft piles.
Players alternate picking a pile, then adding a face-up card to each pile, including one to replace the pile they chose. The draft ends when all the cards are drafted.
The piles have no maximum size.
alternate setup:
Each player opens their 3 boosters and shuffles them together (removing any basic lands first.) Each player deals off 2 face up cards to create the piles, 4 total and players still choose from any pile. After each choice, both players add 1 face-up card to each of 'their' piles from their draft deck/pool.
Deck Building
Nominally a normal 40-card limited deck is suggested for these formats; this leads to rather low power/'bad' decks, bad mana bases, etc.
I would suggest 30-card decks for better game play (n.b. some people consider the low power-level of the 40-card decks very skill testing and part of the fun.)
You should decide the minimum deck size before drafting.
Players build a deck of the agreed size, using their draft picks and as many basic lands as they need.
Play
The player who drafted second gets the choice to play or draw in the first game of the match. A match is usually a race to 2 wins (nominally best 2 of 3, but draws can force additional games!)
Re-playability
When the match is over you can shuffle up and draft again, or try another format. Since the cards come off the draft deck in a random order, each draft will be different.
If new packs were used, these can be saved to draft again, or combine 2 or more draft pools to choose a random (90 card) subset for better re-playability.