How would I do it?
1. Move your awkward guys, your potential guys who haven't yet made it, your guys who don't 'look the part' over to Smackdown. Keep Raw for Cena, Orton, Miz, Jomo, Triple H etc.
2. Make the conscious decision that Raw is the show for more mainstream audiences, PG friendly and where the next handsome face superman character or whatever happens. Raw will sell merch, and that's great. But if Raw is where you make the next Cena, make Smackdown where you will see the next Mick Foley shine. Think of the stars who have been made by groups/gimmicks that you could consider mainstream friendly and the ones that are more awkward and 'edgy' and in my opinion, you get a rough 50-50 through history. WWE unfortunately doesn't currently have somewhere where a new brood, dx, ministry or nation of domination could happen organically like they did in the attitude era. But I suspect that if...
3. You encourage wrestlers to try and emphasise what makes them different or controversial, you could end up with more Triple Hs instead of Hunter Hearst Helmsleys and Stone Colds instead of Ringmasters. Look at Cody at the moment to see how perfectly it can happen.
4. Bring back an approach that will let wrestlers look different. Masks, facepaint, costumes. The only things that currently distuingishs between people these days is... whether they wear trunks or trousers, whether they are black or white. The best loved wrestlers are the larger than life characters, not people just trying to be like you and I. Hulk tore his shirt off. Stone Cold would ride in on a beer truck. Sting was a ghost. Undertaker was a horror movie. Ric Flair was a playboy. Ultimate Warrior was mental. Mankind was... well, you get the picture. And yes, I think a Ultimate Warrior would work today as there is so little done to get crowds hyped up or interact with them that they'd eat out of your hands for the guy who runs around high fiving kids and going bezerk at heels who go against the crowd or what they stand for. The closest you have today is Mysterio whispering something in kids ears, more like a guidance councellor than someone who is going to make the crowd go crazy.
5. Take away a lot of the hell in a cell, ladder matches etc. and instead of put an emphasis on proper wrestling matches with simple stories being told in a match, usually between good and evil. Watching No Holds Barred stuff with no blood or VIOLENCE just turns people off, imo, but make it a wrestling generation of actual competition to compete with MMA and you'd have a hook. Make matches last 30 minutes plus to establish stars to be reckoned with. Whoever fought Flair in those 60 minute ties instantly became a star, not how good they were at promos. If you saw Bryan or Cody or McIntyre go 45 minutes and make every second interesting, you'd be telling your friends. If they just shot a good promo, you'd like it but not enough to go shouting about it.
6. Bring back managers for obvious stars who suck at promos (hey John Morrison), make other wrestlers who can't talk take a backseat. Hell make them work on it, like take a local improve class once a week or something.
7. Bring back stables. It will instantly make the tag team division more interesting and give new guys a chance. The likes of The Rock, Undertaker, Kevin Nash as Diesel, Randy Orton, Triple H, Mr. Perfect, JBL, the Hart family - these guys became names under other people's gimmicks, stables and so on. It gives young guys room to learn, to see who rises to the top (look at Heath Slater compared to Wade Barrett) on who can hold down a team with promos and wrestling ability.
8. Reuse old successful gimmicks. Look at how great the long, sustained run up was with Goldberg. Give your funny rebels a DX. Del Rio is currently riding the DiBiase money train to success. How about Zach Ryder as a cocky heartbreak kid type? What about Drew McIntyre as the most dangerous man in the world ala Ken Shamrock? I'm not saying use the same tag lines but gimmicks have been essential in the past and could help so many people get over if they just let people play a character again.
9. Stick to storylines. If someone is a strong heel who doesn't initially get crowd heat, don't decide that is for a reason and have him be taken out. If you were to take the Goldberg route, say with Kong going through every female wrestler, have her do so until she gets the title and then hold on to it until someone else working hard for the push to take her out. Don't have the character fall before they hit that target (Del Rio has lost SO MUCH heat thanks to losing at Wrestlemania and crying about a broking window, that if one can afford 7000 classic cars, should not really be a problem).
10. Work with Sin Cara on learning English and not botching that trampoline thing.
11. Enjoy it.