Nintendo is sending emails with codes for the demo, though who they send them too is mostly random. Each email has two codes, one for the recipient or one for a friend. Signing up for My Nintendo, the company’s rewards program, is presumably necessary, and making friends with someone else who’s signed up for it can’t hurt.
You can also buy a demo. As part of this week’s E3 Digital Ticket Humble Bundle, a code for Generations is one of the second tier rewards, meaning you’ll get it along with a ton of other goodies for only 4 dollars. If you can’t wait to hunt monsters, than that’s your safest bet.