How are they going to, or how should they?
I'll try answering the former with the incomplete amount of info we have. Brand saturation. I think that the NX will be fine hardware wise, but I think what Nintendo is truly ramping up to do is make their brand relevant and mainstream again. Not Mario. Not Pokemon. Nintendo.
They are going to start with the mobile games and the most important bit, which is the new membership program. They are going to use both in tandem with one another to rapidly spread brand awareness and get as many people signed up as possible to the program through the initial game.
I think they'll announce more media partnerships down the road, including a television show/feature film. Those will also try and connect people to the new membership program. By this time next year, the momentum will already have shifted in Nintendo's favor as most of these announcements will be made including the NX and Nintendo's mobile games successful.
The NX will be advertised heavily in tandem with the new membership program, the one of which tens of millions of people will be apart of. The mobile game will be a fad, definitely, but a much more organized and controlled fad than what the Wii was, and with longer legs.
Once people are acclimated to the new Nintendo ecosystem, they will be introduced to the NX. Just by pure brand exposure, it will launch successfully. That's never been the issue. The longevity will come from how good the tech is, which is up in the air, how good the UI experience is, which I think will be Nintendo's best work yet and something honestly revolutionary for the industry, and how integrated it is to the membership program, which is obviously the primary point of it.
And obviously the games. But I really think the most important thing to the NX's success will be it's firmware. The NX will live or die by how well it connects, from launch, to everything. At launch, it needs to have seamless and innovative connections to mobile through the membership program. At launch, it needs to have perfect integration between the NX and NXDS, even if that means delaying one of them behind the scenes.
People don't want to hear it, or at least they like to underplay it, but that dichotomy between playing all your console games on the go and then seamlessly at home is what will send NXs flying off shelves, but it has to be perfect at launch. If someone wants to just own the NXDS and that's it, 95% of those games all need to be playable there without a hitch. If someone owns both, they need to be able to seamlessly interchange between both.
If I start Zelda U on my NX at home, I need to be able to save, shut it off, take my NX on the train, and continue playing without even thinking about it. If it's not that seamless, at launch, the NX fail.
That means that the NX needs to have perfect cloud support so that cross saves are effortless, the NXDS needs to have a taxed data plan that is "free" to the consumer, the membership program integration needs to be perfect between both devices, and cross-buy needs to be implemented without a hitch. And much more. If it isn't perfect, it will fail. If it is perfect, it will be revolutionary.