Now is the time to do EV training, because you get double EV points and it goes a lot faster. To spread Pokerus, keep one infected Pokemon in your party and go battle, As you battle, the Pokerus will spread to other members in your party. The Pokerus "goes away" in 2-3 days, meaning that you'll still enjoy its benefits, but it will no longer spread.
Keep that second infected Pokemon in your PC because Pokerus will remain active indefinitely as long as it's in your PC storage. Take it out only when you want to infect other Pokemon. As for EV training itself, it's not hard. Just defeat Pokemon that give you the EV's you want and run from everything else. Make sure that the Pokemon you want to EV train either holds the Exp. Share or appears sometime during each battle.