A lot of poorly taped seasons on the intertrons, dvd ppv's for the major WWE shows and written records. I've caught up on a lot of it but I hadn't even heard of WCW until that year when people started marking out left and right.
Some things I think you must see:
Stone Cold's run from the Summer of 1996 to the Summer of 1997. It's fucking awesome. Especially at the beginning when he stood out so much from everything else going on in the WWF. The neck injury happened in the Summer of 1997, on top of the knee injury, and he wasn't quite the same again, but before that he was amazing.
The Sandman/Tommy Cairo feud with led into the Dreamer/Sandman feud which then bled into the Raven/Dreamer feud. For my money, I think the tail end of the Cairo/Sandman and into Dreamer/Sandman was the best feud ECW ever did. Raven/Dreamer is good, but I've always felt Dreamer/Sandman was better. And actually, I think Raven/Sandman was better than Dreamer/Raven. Basically you need to watch most of ECW 1994-1995 since all of those feuds are connected and interwoven, plus you'll get a lot of good stuff with Eddie/Dean/Benoit/Eliminators/Jericho/Scorpio/random Japanese dudes. There is also the Taz/Sabu feud, which was pretty much all of 1996 and 1997.
For WCW, you need to see the Dustin Rhodes vs Studd Stable feud, for starters. You might also want to dip back into the Dangerous Alliance era if you missed it, because that shit was awesome. Vader vs Sting, any Hollywood Blondes you can get a hold of, the 1995 Savage/Flair feud which I think was their best work together, the Sting/Luger storyline where Lex was a heel and Sting was a face but they were still bros, pretty much any midcard stuff from early 1996 to 1999, late Spring of 1996-Fallish of 1996 for nWo stuff then skip ahead to Fall of 1997 because it's exactly the same shit for that whole year. All the cruiser/tag/hardcore stuff for the first 4-5 months of 1999 were really good.
It's really a massive amount of stuff to watch. I think the best way to watch it is to actually watch all the weekly shows. Complete years worth of main WCW/WWF shows and PPVs are pretty easy to find online from 1995/1996 on. Not totally sure about ECW. It's pretty much impossible to find full years of WCW shows before Nitro came along. It's just such a commitment and if you watch a whole year of shows, you aren't really that excited to watch another 80 gigs of shows right away.
I wish WWE did more full feud comps. They don't need the shoot interviews like Bret vs HBK. Just a full chronicle of promos and matches from specific feuds. I'd much rather get something like that than DVDs produced on one guy. I want a god damn Dustin vs Studd Stable DVD, god damnit. I want a Randy Savage vs Ric Flair 1991-1999 DVD, god damn it. I want a Raven vs Dreamer vs Sandman DVD, god damn it. I want a Sting vs the Dangerous Alliance DVD, god damn it. I want a Bret vs Stone Cold DVD, god damn it.
GOD DAMN IT.