The best way to encourage your happy customers to leave positive reviews for you is to simply ask. You should also make it as easy as possible to do so. Ask for testimonials and display them in a prominent place on your website.
This will make new customers think more about the positive attributes of your business. The problem with testimonials on your website is that people don’t often believe they are genuine, even if they in fact are. Use a 3rd-party review provider that can verify customer independantly and embed your review custom page in the top menu. Do the same and embed widgets in various pages of your website: on the first page or on your cart page, if any.
Also ask for reviews on social media and various 3rd party review sites. These usually come across as more trustworthy to potential new customers. You can encourage people to give feedback on the review and social media sites that you select by sending out review invitations and selecting a few review sites where you'd like customer feedback.
Easy access to your Facebook Review page and Review sites thanks to review invitations make it more probable that a customer who has had a good experience will share feelings on popular social and review platforms where they can be seen by others.