Both Flash and Green Lantern have long histories, so I'm going to focus on recent stepping-on points, per the question's request. For Green Lantern, it's pretty straightforward. There was a recent Secret Origins story in Green Lantern, which is as good a time as any to hop on. Apparently they re-released it with a new cover to promote the movie. If you're interested in reading more, then I recommend starting with the current run of Green Lantern. The first of these is here, and that starts the regular Green Lantern book over with a sort of fresh start after some recent shake-ups. If you want to dig back into that history, I'd recommend waiting until you've read the Sinestro Corps War story, as that includes some crucial pieces of historical information.
Now then, there are 2 main Green Lantern books at that point in history, the one above and Green Lantern Corps, which had a new number 1 issue around the same time. Unlike the main Green Lantern book, I think the mini-series that relaunched Green Lantern Corps is pretty easy to read for beginners, and you can find that here. After reading that book, pick up Green Lantern Corp Vol 1, then 2 and so on. Green Lantern Corps and Green Lantern run in parallel, with minimal crossover. The previously-mentioned Sinestro Corps War is the first big crossover between them.
The Flash has had a rough past few years. The character who is the main Flash changed a few times, and there have been a couple of relaunches of the Flash comic book as a result. I think your best bet here is to start reading the current Flash book. This one is pretty recent, roughly a year old, you can find the first volume here. It starts with a solid introduction to the new main Flash and his family of friends and rogues gallery.
Both Green Lantern and The Flash hold key places in the DC Universe. The Green Lantern Corps was started by the Guardians of the Universe, ancient aliens who have lived for eons. Events they participated in at the dawn of the universe resulted in the creation of the Corps. If you find you like Green Lantern, you can read more about the Corps' history in the Tales of the Green Lantern Corps reprints they've been publishing (see here). The Flash kicked off the Silver Age, and decades later the Flash's contribution to the Crisis on Infinite Earths stood as a marker in superhero history. Once you're familiar with the Flash, I recommend you read Crisis on Infinite Earths. It's an epic and will provide some crucial history to the Flash.
If you want to read old-school tales of both these heroes, you can find those in DC's Showcase collections. They're thick books that collect Silver-Age stories for low prices. However, these have a decidedly different tone and story-telling style compared to the modern stuff.