Honestly just start checking out the Rebirth one-shot and different series coming out of it that interest you. It's a big jumping on point for new and returning readers, and I've seen it succeed on both those points.
If.you want to learn more though, I suggest asking your FLCS guy/gal when you're in to pick up stuff.
While the Rebirth line is easy to jump into, it can be nice to know what's been the DC universe's storyline over the last few years. That seems to be what he's asking about so he knows, not just for the sake of new reading.
Can anybody recommend a website (not wikipedia) that summarizes all the "recent" changes to the DC universe? Last thing I really read was Brightest Day. But since then there's been One Year Later, 52, a new 52, and now rebirth? I have no idea what this stuff means really, and I don't want to go by 47 trades to catch up.
I can try to summarize the gist of it. A lot of it has to do with mixing, creating, and ending timelines, and since various tie-ins have their own storylines, the main events don't get into everyone's details. That said, focusing on what I consider to be the characters of major import--The Flash and Superman--here's my rundown:
- Flashpoint: Barry Allen wakes up in a distorted timeline. Long story short, he's the cause of it, by going back in time to save his mother. He corrects the timeline, but the events seem to have affected the multiverse.
- NU52: Not so much an event, but part of a consequence involving Flashpoint. In the real world, this was to reset all the comics back to square one. But it didn't actually do that. All the heroes just think things are a certain way. Many of them never met each other, so we see the Justice League formed for the first time, villains met or reimagined, etc. Essentially a more simplified status quo ... or so it would seem. Important point: Wally West is a different person here than in pre-Flashpoint.
- Convergence: DC universe characters from many ruined worlds and timelines are brought to a planet to fight each other and show who is strongest, a la DC equivalent of Battleworld. The core of this involves Braniac, but essentially those who won get a free pass to live in the NU52 universe. Among those plucked out of their situation are the old universe's Superman, Lois Lane, and their son Jon Kent. NU52 Superman never went through the stuff we saw Superman deal with back in the 90s. The guy who got "killed" by Doomsday in The Death of Superman? That's this one. After Convergence, he, Lois, and Jon hide out on NU52 Earth as the Smith family.
- The Last Days of Superman: Due to various events, NU52 Superman is dying. I was never into the NU52, so I don't know much about him except he was a jerk and in a relationship with Wonder Woman, not Lois Lane. He's assisted by a man with similar powers to himself at times, and when NU52 Superman dies, it's revealed that this man is actually pre-Flashpoint Superman, the original one who's been hiding out since Convergence.
- DC Rebirth: Turns out that the Wally West of pre-Flashpoint was not erased by the NU52. He's actually been in the Speedforce. He can feel himself slipping away, so tries to break through into NU52, but no one remembers him until he meets up with Barry Allen. When they touch, Barry's memories return from before NU52. It's become clear that some malevolent entity capable of rewriting reality and memories has severely altered the DC universe in the wake of Flashpoint (i.e. an in-universe explanation for DC's 2011 reboot NU52, so any retcon can now can be explained as the result of this entity). Wally decides to link up with the Titans so they can figure out who caused all this, while Barry Allen and Bruce Wayne investigate to see what they can come up. Meanwhile, pre-Flashpoint Superman, known as Clark Smith instead of Clark Kent, takes up the proper mantle of Superman and is trying to adjust to a world that looks similar, but is actually very different from the one he knew.
I think that summarizes the important points from Brightest Day to now. There were other events, but from what I can tell those are the ones that have shaped current events.