Two motivations are: (1) To be heard and (2) to pay it forward.
If you have a big enough platform, your users will spout off their opinion for no reward other than social validation.You can start this off by seeding your reviews. (ie. beg your friends and early customers to write reviews) If new users see fresh reviews, they will be less shy about writing their own.
The other strategy is to send a follow-up email after each purchase, with a simple up-or-down question and two big buttons. "Did you enjoy [____]?" with two side-by-side buttons (thumbs up/thumbs down). After they click, take them to a very simple, focused landing page where they can write a quick review. You tell them it's to help other people just like you learn more about this product or service by sharing your experience.
Combine the two as needed.