Two scenarios I have heard are:
1 - Every team has the same chance (1 lottery ball per team)
2 - Weighted lottery based on the teams perfomance and playoff history the last 4 years. For example, the NY Rangers will 4 lottery balls (missed last 4 playoffs), while the Maple Leafs would have only one (the made the playofss each of the last 4 yrs), and a team like the Montreal Calgary Flames would get 3 ( they only made the playoffs 1 in 4 years) In addition to the these 2 scenarios, the word is the may flip and reverse the order every round (i.e.) Leafs pick #30 in round 1(last pick of round 1), and #31 in round 2 (first pick of the 2nd round).
What would I pick?
I would pick scenario #1. Why you ask? Simple, it would casue an enormous amount of excitement for the NHL and would potentially spark a lot of trades and shuffling around in the draft order.