The "God particle" is the single most annoying name for it ever. I'm fairly sure that the intended title for the book from which the Higgs Boson gets its name was "the *** particle" -- because of all the resources that had gone into finding it that had, until that point, been unsuccessful.
Anyway, we found it and a discovery of a Higgs boson-like particle was announced in July 2012. Since then, the LHC has been largely devoted to analysing the full data gathered in its first few years of operation, as the current run is still in its early days -- probably the first results from 2015 experiments will be released early next year.
From the old data, anyway, there's been plenty of things to provide interest to the physics community, but nothing particularly spectacular or solid yet. Mainly, what's come out has been further confirmation of the success of the "Standard Model", whereas actually physicists were kind of hoping that something would be found to be wrong with it. We'll see what the next few years bring.
The "experiment" itself remains basically the same: smash two protons together and see what gets spat out. The challenge is to sort out the interesting stuff from the dross, and it's not really possible to describe just how remarkable it is that we've been able to do this effectively.