The storms will arrive along with the update, but we don’t have a specific date as of yet. We just know the update will arrive sometime this month. These storms will actually roam between star systems using the gate network. That’s not intimidating at all.
As for what specifically these storms will do, well,
“The wandering weather will apply system effects, not unlike those seen in wormhole space and Abyssal Deadspace, with a core of systems that contain the strongest effects, as well as a periphery of additional star systems exhibiting weaker versions of those effects, also.”
As expected, they’ll have an effect on vessels, while also providing Capsuleers with some new challenges. As noted in the forums, while the core of these storms will remain in nullsec, be warned that their effects can “spill over” into nearby lowsec and highsec systems. Additionally, CCP provides in-depth statistics for each type of storm, their effects, and their buffs.