TRADES: Between NFL and AFL teams? No. Seeing as how these are competing leagues, there's no way they'd voluntarily do that.
DRAFT: The drafting proces would go much as it did in the 60's; both league would have their own drafts, then their respective teams would most likely try to outbid the other for the picks they selected. For exhample, a player picked #1 overall in both the NFL and AFL could choose which contract to sign.
FREE AGENCY: Odds are, the fierce competition for Blue Chip athletes would force an earlier birth of Free Agency in a bid to dry up the other's well. In fact, I would wager the AFL would've been the first to embrace this move as a means to fight the NFL into the 70's or even 80's.