I think it is a Constitutional Amendment. You amend the Constitution either with 2/3's of Congress or with state legislatures from states with 2/3's of the electoral vote. That proposal is currently going through the state legislatures. Cohen's bill is the other track.
I too think the state legislature approach is more likely to succeed. If you look at my link, there are enough blue and purple states who haven't yet enacted to pass it. Just add in Maine, New Hampshire, Pennsylvania, Michigan, Wisconsin, Minnesota, Oregon, Nevada, Colorado, Virginia and New Mexico and we're over the top. We don't even need the now red leaning Ohio or the impossibly screwed up North Carolina.