DC Comics has gotten into a good habit in recent years in making its events fairly easy to follow, with one main book and a limited group of supporting titles. Final Crisis, for instance, was pretty much completely contained to books that actually carried the "Final Crisis" banner, and Blackest Night will be similar.
Similar to Sinestro Corps War, Blackest Night will unfold a lot of its story in the regular Green Lantern books, Green Lantern and Green Lantern Corps. Unlike Sinestro Corps War, however, there's also going to be the eight-issue Blackest Night book. Although the three titles will likely focus on different aspects of what is, after all, a universe-spanning war, you're probably going to need to read at least these three books if you want to follow the story coherently. And, even if you're planning skipping all other previous stories, it would probably be helpful to read last week's Green Lantern #43, which serves as the official prologue for Blackest Night.
To help get readers caught up on the admittedly complicated backstories of the different Corps, this month will also feature three issues worth of Blackest Night: Tales of the Corps. These books will, among other things, finally reveal some concrete details on the Indigo Tribe, easily the most mysterious and unexplored of the various factions.
There are also three supporting mini-series highlighting how the Blackest Night affects some of the most prominent characters in the DC universe. Blackest Night: Batman, Blackest Night: Superman, and Blackest Night: Titans all begin in August, and all three promise to reunite the characters with their deceased loved ones in the most heartbreaking fashion imaginable. (Four words: Pa Kent, Black Lantern.) After these finish up in October, there will be a second trio of mini-series to accompany the second half of Blackest Night. These will be Blackest Night: Wonder Woman, Blackest Night: Flash, and Blackest Night: JSA.
The exact checklist for the entire run hasn't been revealed yet, but here's everything you need for the first three months, assuming no delays (which is admittedly quite an assumption):
July 8: Green Lantern #43
July 15: Blackest Night #1, Blackest Night: Tales of the Corps #1
July 22: Green Lantern #44, Blackest Night: Tales of the Corps #2
July 29: Blackest Night: Tales of the Corps #3
August 12: Blackest Night #2, Green Lantern Corps #39, Blackest Night: Batman #1
August 19: Blackest Night: Superman #1
August 26: Green Lantern #45, Blackest Night: Titans #1
September 9: Green Lantern Corps #40, Blackest Night: Batman #2
September 16: Blackest Night #3
September 23: Blackest Night: Superman #2
September 30: Green Lantern #46, Blackest Night: Titans #2
[Note: DC should be releasing their October solicitations in the very near future, so I'll update this once I have the exact dates for the October books.]