>>87123364read LoSH 6 in order, but don't forget the february 2011 annual and the Legion of Super Villains Special, which you should read some time around May 2011.
Parallel to that, read Adventure Comics Vol 2, which gets renamed back to Adventure Comics Vol 1 again halfway through. Adventure Comics starts out with a focus on Superboy (Con-El), but shortly switches to early Legion adventures with the "real" Superboy again.
When this is over, Flashpoint hits. It doesn't relate to the Legion at all, as far as I remember not a single one shows up.
After Flashpoint, read LoSH VOl 7 and Legion Lost, which crosses over into Teen Titans and I think even The Ravagers in the end and culminates in a shitty finish.
Now we have another killing event for the Legion, which finishes that run completely, too.
There is a 6 issue mini-series crossover with Star Trek, called Star Trek/Legion of Super-Heroes (how inventive). Read it, it's really good, especially if you know stuff about Star Trek and generally have watched pretty much any kind of time travel shenannigans series on tv.
Then the Legion is regularly over so far, but it shows up in a few of the new Action Comics issues again (05, 06 and 16-18), then there's Convergence - Superboy and the Legion of Super-Heroes plus the Blue Beetle and Booster Gold issues and finally Justice League United (read 05, then the JLU Annual, then 06-10), which wraps up New52's Legion.
Also there are a few issues of Booster Gold that tie into Legion stuff, vol 1 08 and 09 and vol 2 01 (I think it's where Brainiac wants to find out why the fuck Booster has a Legion Flight Ring), 02 and 03 only have Infectuous Lass in it but I can't remember what happens so I guess you can skip it, 10, 32 (this one ties retroactively into The Great Darkness Saga, so don't skip it) and 43.
Also if you like to expand your horizon, there's also L.E.G.I.O.N. and R.E.B.E.L.S., which is a different tale though.
And that about finally wraps it up.
