Pokemon only catch Pokerus randomly through battling and/or catching wild Pokemon. It's an incredibly rare chance to catch it. If you do get it & go to heal up the PKMN centre, Nurse Joy will notify you saying that your Pokemon has caught Pokerus.
>Pokérus has a 3 in 65,536 chance of being generated on a Pokémon, either wild or bred.
Pokerus is also 'healed' if your game goes past midnight and the Pokemon with the disease is not in the PC. If they stay in the PC, they will have Pokerus for an indefinite amount of time (until you leave it in your party past midnight) and can pass it on to others.
Best thing to do is probably ask for a Pokerus infected Pokemon in a trade. It takes an insane amount of time to actually get Pokerus through random battling unless you're incredibly lucky.